Publications and preprints

Preprints

1. Singular Kähler-Einstein metrics on Q-Fano compactifications of Lie groups, Yan Li, Gang Tian, Xiaohua Zhu (Posted on January 30, 2020. Downloads:   )

In this paper, we prove an existence result for Kähler-Einstein metrics on Q-Fano compactifications of Lie groups. As an application, we classify Q-Fano compactifications of $SO \sub 4 (C)$ which admit a Kähler-Einstein metric with the same volume as that of a smooth Fano compactification of $SO \sub 4 (C)$.

2. Almost Hermitian Ricci flow, Casey Lynn Kelleher, Gang Tian (Posted on January 18, 2020. Downloads:   )

We introduce a new curvature flow which matches with the Ricci flow on metrics and preserves the almost Hermitian condition. This enables us to use Ricci flow to study almost Hermitian manifolds.

3. Normality of Circular β-ensemble, Renjie Feng, Gang Tian, Dongyi Wei (Posted on May 23, 2019. Downloads:   )

We will prove the Berry-Esseen theorem for the number counting function of the circular β-ensemble (CβE), which will imply the central limit theorem for the number of points in arcs. We will prove the main result by estimating the characteristic functions of the Prüfer phases and the number counting function, which will imply the the uniform upper and lower bounds of their variance. We also show that the similar results hold for the Sine$\sub{beta}$ process. As a direct application of the uniform variance bound, we can prove the normality of the linear statistics when the test function $f(\theta)\in W^{1,p}(S^1)$ for some $p\in(1,\infty)$.

4. A wall-crossing formula and the invariance of GLSM correlation functions, Gang Tian, Guangbo Xu (Posted on May 13, 2019. Downloads:   )

In this paper we prove a wall-crossing formula, a crucial ingredient needed to prove that the correlation function of gauged linear sigma model is independent of the choice of perturbations.

5. Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow, Jian Song, Gang Tian, Zhenlei Zhang (Posted on April 17, 2019. Downloads:   )

We prove a uniform diameter bound for long time solutions of the normalized Kahler-Ricci flow on an n-dimensional projective manifold X with semi-ample canonical bundle under the assumption that the Ricci curvature is uniformly bounded for all time in a fixed domain containing a fibre of X over its canonical model $X\sub{can}$. This assumption on the Ricci curvature always holds when the Kodaira dimension of X is n, n−1 or when the general fibre of X over its canonical model is a complex torus.

6. On the existence of conic Kahler-Einstein metrics, Gang Tian, Feng Wang (Posted on March 29, 2019. Downloads:   )

In this paper, we prove the conic version of YTD conjecture on log Fano manifolds.

7. The uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties, Chi Li, Gang Tian, Feng Wang (Posted on March 4, 2019. Downloads:   )

We prove the following result: if a Q-Fano variety is uniformly K-stable, then it admits a Kähler-Einstein metric. We achieve this by modifying Berman-Boucksom-Jonsson's strategy with appropriate perturbative arguments and non-Archimedean estimates. The idea of using the perturbation is motivated by our previous paper.

8. Small gaps of GOE, Renjie Feng, Gang Tian, Dongyi Wei (Posted on January 6, 2019. Downloads:   )

In this article, we study the smallest gaps of the Gaussian orthogonal ensemble. The main result is that the smallest gaps, after normalized by n, will tend to a Poisson distribution, and the limiting density of the k-th normalized smallest gaps is $2x^{2k-1}e^{-x^2}/(k−1)!$.

9. On uniform K-stability of pairs, Gang Tian (Posted on December 14, 2018. Updated on Dec 14, 2018. Downloads:   )

In this paper, we discuss stable pairs, which were first studied by S. Paul, and give a proof for a result I learned from him. As a consequence, we will show that the K-stability implies the CM-stability.

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More preprints can be found on:

http://arxiv.org/find/grp_math/1/au:+tian_gang/0/1/0/all/0/1


Selected publications

1. Feng, Renjie; Tian, Gang; Wei, Dongyi. Spectrum of SYK Model. Peking Math. J. 2 (2019), no. 1, 41–70.

2. Feng, Renjie; Tian, Gang; Wei, Dongyi. Small gaps of GOE. Geom. Funct. Anal. 29 (2019), no. 6, 1794–1827.

3. Li, Chi; Tian, Gang. Orbifold regularity of weak Kähler-Einstein metrics. Advances in complex geometry, 169–178, Contemp. Math., 735, Amer. Math. Soc., Providence, RI, 2019.

4. Bellettini, Costante; Tian, Gang. Compactness results for triholomorphic maps. J. Eur. Math. Soc. (JEMS) 21 (2019), no. 5, 1271–1317.

5. Tian, Gang. Some progresses on Kähler-Ricci flow. Boll. Unione Mat. Ital. 12 (2019), no. 1-2, 251–263.

6. Shi, Yuguang; Sun, Jiacheng; Tian, Gang; Wei, Dongyi. Uniqueness of the mean field equation and rigidity of Hawking mass. Calc. Var. Partial Differential Equations 58 (2019), no. 2, Art. 41, 16 pp.

7. Tian, Gang; Wei, Dongyi. Asymptotic of Enumerative Invariants in CP2. Peking Math. J. 1 (2018), no. 2, 125–140.

8. Naber, Aaron; Tian, Gang. Geometric structures of collapsing Riemannian manifolds II. J. Reine Angew. Math. 744 (2018), 103–132.

9. Tian, Gang; Xu, Guangbo. Analysis of gauged Witten equation. J. Reine Angew. Math. 740 (2018), 187–274.

10. Tian, Gang. K-stability implies CM-stability. Geometry, analysis and probability, 245–261, Progr. Math., 310, Birkhäuser/Springer, Cham, 2017.

11. La Nave, Gabriele; Tian, Gang; Zhang, Zhenlei. Bounding diameter of singular Kähler metric. Amer. J. Math. 139 (2017), no. 6, 1693–1731.

12. Tian, Gang; Xu, Guangbo. The symplectic approach of gauged linear $\gamma$-model. Proceedings of the Gökova Geometry-Topology Conference 2016, 86–111, Gökova Geometry/Topology Conference (GGT), Gökova, 2017.

13. Tian, Gang. A third derivative estimate for Monge-Ampere equations with conic singularities. Chin. Ann. Math. Ser. B 38 (2017), no. 2, 687–694.

14. Song, Jian; Tian, Gang. The Kähler-Ricci flow through singularities. Invent. Math. 207 (2017), no. 2, 519–595.

15. Tian, Gang. Notes on Kähler-Ricci flow. Ricci flow and geometric applications, 105–136, Lecture Notes in Math., 2166, Springer, [Cham], 2016.

16. Tian, Gang; Zhang, Zhenlei. Convergence of Kähler-Ricci flow on lower-dimensional algebraic manifolds of general type. Int. Math. Res. Not. IMRN 2016, no. 21, 6493–6511.

17. Tian, Gang. Futaki invariant and CM polarization. Geometry and topology of manifolds, 327–348, Springer Proc. Math. Stat., 154, Springer, [Tokyo], 2016.

18. La Nave, Gabriele; Tian, Gang. A continuity method to construct canonical metrics. Math. Ann. 365 (2016), no. 3-4, 911–921.

19. Tian, Gang; Zhang, Zhenlei. Regularity of Kähler-Ricci flows on Fano manifolds. Acta Math. 216 (2016), no. 1, 127–176.

20. Song, Jian; Tian, Gang. Bounding scalar curvature for global solutions of the Kähler-Ricci flow. Amer. J. Math. 138 (2016), no. 3, 683–695.

21. Tian, Gang; Xu, Guangbo. Correlation functions of gauged linear $\gamma$-model. Sci. China Math. 59 (2016), no. 5, 823–838.

22. Boileau, Michel; Besson, Gerard; Sinestrari, Carlo; Tian, Gang. Ricci flow and geometric applications. Lecture notes from the CIME Summer School held in Cetraro, 2010. Edited by Riccardo Benedetti and Carlo Mantegazza. Lecture Notes in Mathematics, 2166. Springer, [Cham]; Fondazione C.I.M.E., Florence, 2016. xi+136 pp.

23. La Nave, Gabriele; Tian, Gang. Soliton-type metrics and Kähler-Ricci flow on symplectic quotients. J. Reine Angew. Math. 711 (2016), 139–166.

24. Tian, Gang. Corrigendum: K-stability and Kähler-Einstein metrics. Comm. Pure Appl. Math. 68 (2015), no. 11, 2082–2083.

25. Tian, Gang; Wang, Bing. On the structure of almost Einstein manifolds. J. Amer. Math. Soc. 28 (2015), no. 4, 1169–1209.

26. Tian, Gang; Zhang, Qi S. A compactness result for Fano manifolds and Kähler Ricci flows. Math. Ann. 362 (2015), no. 3-4, 965–999.

27. Tian, Gang. K-stability and Kähler-Einstein metrics. Comm. Pure Appl. Math. 68 (2015), no. 7, 1085–1156.

28. Tian, Gang. Kähler-Einstein metrics on Fano manifolds. Jpn. J. Math. 10 (2015), no. 1, 1–41.

29. Hong, Min-Chun; Tian, Gang; Yin, Hao. The Yang-Mills $\alpha$-flow in vector bundles over four manifolds and its applications. Comment. Math. Helv. 90 (2015), no. 1, 75–120.

30. Tian, Gang. Geometric analysis on 4-manifolds. The Poincaré conjecture, 145–166, Clay Math. Proc., 19, Amer. Math. Soc., Providence, RI, 2014.

31. Streets, Jeffrey; Tian, Gang. Symplectic curvature flow. J. Reine Angew. Math. 696 (2014), 143–185.

32. Tian, Gang; Zhang, Qi S. Isoperimetric inequality under Kähler Ricci flow. Amer. J. Math. 136 (2014), no. 5, 1155–1173.

33. Morgan, John; Tian, Gang. The geometrization conjecture. Clay Mathematics Monographs, 5. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2014. x+291 pp.

34. Tian, Gang. Partial $C^0$-estimate for Kähler-Einstein metrics. Commun. Math. Stat. 1 (2013), no. 2, 105–113.

35. Tian, Gang; Zhang, Zhenlei. Regularity of the Kähler-Ricci flow. C. R. Math. Acad. Sci. Paris 351 (2013), no. 15-16, 635–638.

36. Streets, Jeffrey; Tian, Gang. Regularity results for pluriclosed flow. Geom. Topol. 17 (2013), no. 4, 2389–2429.

37. Tian, Gang; Zhang, Shijin; Zhang, Zhenlei; Zhu, Xiaohua. Perelman's entropy and Kähler-Ricci flow on a Fano manifold. Trans. Amer. Math. Soc. 365 (2013), no. 12, 6669–6695.

38. Nguyen, Luc; Tian, Gang. On smoothness of timelike maximal cylinders in three-dimensional vacuum spacetimes. Classical Quantum Gravity 30 (2013), no. 16, 165010, 26 pp.

39. Neves, André; Tian, Gang. Translating solutions to Lagrangian mean curvature flow. Trans. Amer. Math. Soc. 365 (2013), no. 11, 5655–5680.

40. Tian, Gang; Zhu, Xiaohua. Convergence of the Kähler-Ricci flow on Fano manifolds. J. Reine Angew. Math. 678 (2013), 223–245.

41. Tian, Gang. Existence of Einstein metrics on Fano manifolds. Metric and differential geometry, 119–159, Progr. Math., 297, Birkhäuser/Springer, Basel, 2012.

42. Ding, Changming; Li, Kehua; Tian, Gang. On the limit set maps in semidynamical systems. Georgian Math. J. 19 (2012), no. 4, 655–664.

43. Tian, Gang; Zhang, Zhenlei. Degeneration of Kähler-Ricci solitons. Int. Math. Res. Not. IMRN 2012, no. 5, 957–985.

44. Streets, Jeffrey; Tian, Gang. Generalized Kähler geometry and the pluriclosed flow. Nuclear Phys. B 858 (2012), no. 2, 366–376.

45. Song, Jian; Tian, Gang. Canonical measures and Kähler-Ricci flow. J. Amer. Math. Soc. 25 (2012), no. 2, 303–353.

46. Naber, Aaron; Tian, Gang. Geometric structures of collapsing Riemannian manifolds I. Surveys in geometric analysis and relativity, 439–466, Adv. Lect. Math. (ALM), 20, Int. Press, Somerville, MA, 2011.

47. Streets, Jeffrey; Tian, Gang. Hermitian curvature flow. J. Eur. Math. Soc. (JEMS) 13 (2011), no. 3, 601–634.

48. Chen, X. X.; Tian, G.; Zhang, Z. On the weak Kähler-Ricci flow. Trans. Amer. Math. Soc. 363 (2011), no. 6, 2849–2863.

49. Streets, Jeffrey; Tian, Gang. Regularity theory for pluriclosed flow. C. R. Math. Acad. Sci. Paris 349 (2011), no. 1-2, 1–4.

50. Streets, Jeffrey; Tian, Gang. A parabolic flow of pluriclosed metrics. Int. Math. Res. Not. IMRN 2010, no. 16, 3101–3133.

51. Tian, Gang. Finite-time singularity of Kähler-Ricci flow. Discrete Contin. Dyn. Syst. 28 (2010), no. 3, 1137–1150.

52. Neves, André; Tian, Gang. Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds. II. J. Reine Angew. Math. 641 (2010), 69–93.

53. Chen, Bohui; Tian, Gang. Virtual manifolds and localization. Acta Math. Sin. (Engl. Ser.) 26 (2010), no. 1, 1–24.

54. Paul, Sean Timothy; Tian, Gang. CM stability and the generalized Futaki invariant II. Astérisque No. 328 (2009), 339–354 (2010).

55. Neves, André; Tian, Gang. Existence and uniqueness of constant mean curvature foliation of asymptotically hyperbolic 3-manifolds. Geom. Funct. Anal. 19 (2009), no. 3, 910–942.

56. Mundet i Riera, I.; Tian, G. A compactification of the moduli space of twisted holomorphic maps. Adv. Math. 222 (2009), no. 4, 1117–1196.

57. Chen, Xiuxiong; Sun, Song; Tian, Gang. A note on Kähler-Ricci soliton. Int. Math. Res. Not. IMRN 2009, no. 17, 3328–3336.

58. Tian, Gang; Wang, Shuguang. Orientability and real Seiberg-Witten invariants. Internat. J. Math. 20 (2009), no. 5, 573–604.

59. Rivière, Tristan; Tian, Gang. The singular set of 1-1 integral currents. Ann. of Math. (2) 169 (2009), no. 3, 741–794.

60. Tian, Gang. New results and problems on Kähler-Ricci flow. Géométrie différentielle, physique mathématique, mathématiques et société. II. Astérisque No. 322 (2008), 71–92.

61. Birman, Joan S.; Tian, Gang. Preface [In memory of Xiao-Song Lin]. Commun. Contemp. Math. 10 (2008), suppl. 1, v–vii.

62. Auroux, Denis; Catanese, Fabrizio; Manetti, Marco; Seidel, Paul; Siebert, Bernd; Smith, Ivan; Tian, Gang. Symplectic 4-manifolds and algebraic surfaces. Lectures from the C.I.M.E. Summer School held in Cetraro, September 2–10, 2003. Edited by Catanese and Tian. Lecture Notes in Mathematics, 1938. Springer-Verlag, Berlin; Fondazione C.I.M.E., Florence, 2008. xiv+345 pp.

63. Siebert, Bernd; Tian, Gang. Lectures on pseudo-holomorphic curves and the symplectic isotopy problem. Symplectic 4-manifolds and algebraic surfaces, 269–341, Lecture Notes in Math., 1938, Springer, Berlin, 2008.

64. Kołodziej, Sławomir; Tian, Gang. A uniform $L^{infty}$ estimate for complex Monge-Ampère equations. Math. Ann. 342 (2008), no. 4, 773–787.

65. Tian, Gang; Viaclovsky, Jeff. Volume growth, curvature decay, and critical metrics. Comment. Math. Helv. 83 (2008), no. 4, 889–911.

66. Zhang, Ruo Xun; Tian, Gang; Li, Ping; Yang, Shi Ping. Adaptive synchronization of a class of chaotic systems with uncertain parameters. (Chinese) Acta Phys. Sinica 57 (2008), no. 4, 2073–2080.

67. Chen, X. X.; Tian, G. Geometry of Kähler metrics and foliations by holomorphic discs. Publ. Math. Inst. Hautes Études Sci. No. 107 (2008), 1–107.

68. Sesum, Natasa; Tian, Gang. Bounding scalar curvature and diameter along the Kähler Ricci flow (after Perelman). J. Inst. Math. Jussieu 7 (2008), no. 3, 575–587.

69. Auroux, Denis; Donaldson, Simon; Guillemin, Victor; Mrowka, Tomasz; Tian, Gang. Dedication to Dusa McDuff. J. Symplectic Geom. 5 (2007), no. 1, i.

70. Lu, Guangcun; Tian, Gang. Constructing virtual Euler cycles and classes. Int. Math. Res. Surv. IMRS 2007, Art. ID rym001, 220 pp.

71. Song, Jian; Tian, Gang. The Kähler-Ricci flow on surfaces of positive Kodaira dimension. Invent. Math. 170 (2007), no. 3, 609–653.

72. Morgan, John; Tian, Gang. Ricci flow and the Poincaré conjecture. Clay Mathematics Monographs, 3. American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2007. xlii+521 pp.

73. Qing, Jie; Tian, Gang. On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds. J. Amer. Math. Soc. 20 (2007), no. 4, 1091–1110.

74. Tian, Gang; Zhu, Xiaohua. Convergence of Kähler-Ricci flow. J. Amer. Math. Soc. 20 (2007), no. 3, 675–699.

75. Tian, Gang. Aspects of metric geometry of four manifolds. Inspired by S. S. Chern, 381–397, Nankai Tracts Math., 11, World Sci. Publ., Hackensack, NJ, 2006.

76. Ding, Weiyue; Liu, Jiaquan; Tian, Gang. On the occasion of the seventieth birthday of Professor Chang Kung-Ching. J. Partial Differential Equations 19 (2006), no. 3, 193–199.

77. Tian, Gang; Zhang, Zhou. On the Kähler-Ricci flow on projective manifolds of general type. Chinese Ann. Math. Ser. B 27 (2006), no. 2, 179–192.

78. Chen, Xiuxiong; Lu, Peng; Tian, Gang. A note on uniformization of Riemann surfaces by Ricci flow. Proc. Amer. Math. Soc. 134 (2006), no. 11, 3391–3393.

79. Chen, X. X.; Tian, G. Ricci flow on Kähler-Einstein manifolds. Duke Math. J. 131 (2006), no. 1, 17–73.

80. Cheeger, Jeff; Tian, Gang. Curvature and injectivity radius estimates for Einstein 4-manifolds. J. Amer. Math. Soc. 19 (2006), no. 2, 487–525.

81. Cao, Huai-Dong; Tian, Gang; Zhu, Xiaohua. Kähler-Ricci solitons on compact complex manifolds with $C_1(M)>0$. Geom. Funct. Anal. 15 (2005), no. 3, 697–719.

82. Shi, Yuguang; Tian, Gang. Rigidity of asymptotically hyperbolic manifolds. Comm. Math. Phys. 259 (2005), no. 3, 545–559.

83. Tian, Gang; Viaclovsky, Jeff. Moduli spaces of critical Riemannian metrics in dimension four. Adv. Math. 196 (2005), no. 2, 346–372.

84. Siebert, Bernd; Tian, Gang. On the holomorphicity of genus two Lefschetz fibrations. Ann. of Math. (2) 161 (2005), no. 2, 959–1020.

85. Tian, Gang; Viaclovsky, Jeff. Bach-flat asymptotically locally Euclidean metrics. Invent. Math. 160 (2005), no. 2, 357–415.

86. Cheeger, Jeff; Tian, Gang. Anti-self-duality of curvature and degeneration of metrics with special holonomy. Comm. Math. Phys. 255 (2005), no. 2, 391–417.

87. Tian, Gang. An equivariant version of the K-energy. Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 1, 1–8.

88. Chen, Xiuxiong; Tian, Gang. Partial regularity for homogeneous complex Monge-Ampere equations. C. R. Math. Acad. Sci. Paris 340 (2005), no. 5, 337–340.

89. Chen, Xiuxiong; Tian, Gang. Uniqueness of extremal Kähler metrics. C. R. Math. Acad. Sci. Paris 340 (2005), no. 4, 287–290.

90. Hong, Min-Chun; Tian, Gang. Asymptotical behaviour of the Yang-Mills flow and singular Yang-Mills connections. Math. Ann. 330 (2004), no. 3, 441–472.

91. Lu, Zhiqin; Tian, Gang. The log term of the Szegő kernel. Duke Math. J. 125 (2004), no. 2, 351–387.

92. Tian, Gang. Some regularity problems of stationary harmonic maps. Noncompact problems at the intersection of geometry, analysis, and topology, 245–252, Contemp. Math., 350, Amer. Math. Soc., Providence, RI, 2004.

93. Paul, Sean T.; Tian, Gang. Analysis of geometric stability. Int. Math. Res. Not. 2004, no. 48, 2555–2591.

94. Rivière, Tristan; Tian, Gang. The singular set of J-holomorphic maps into projective algebraic varieties. J. Reine Angew. Math. 570 (2004), 47–87.

95. Hong, Min-Chun; Tian, Gang. Global existence of the m-equivariant Yang-Mills flow in four dimensional spaces. Comm. Anal. Geom. 12 (2004), no. 1-2, 183–211.

96. Tao, Terence; Tian, Gang. A singularity removal theorem for Yang-Mills fields in higher dimensions. J. Amer. Math. Soc. 17 (2004), no. 3, 557–593.

97. Arezzo, Claudio; Tian, Gang. Infinite geodesic rays in the space of Kähler potentials. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 4, 617–630.

98. Tian, Gang; Zhou, Jian. Quadratic recursion relations of Hodge integrals via localization. Acta Math. Sin. (Engl. Ser.) 19 (2003), no. 2, 209–232.

99. Tian, Gang. Analytic aspects of Yang-Mills fields. Recent progress in computational and applied PDEs (Zhangjiajie, 2001), 183–194, Kluwer/Plenum, New York, 2002.

100. Tian, Gang. Geometry and nonlinear analysis. Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), 475–493, Higher Ed. Press, Beijing, 2002.

101. Tian, Gang. Elliptic Yang-Mills equation. Proc. Natl. Acad. Sci. USA 99 (2002), no. 24, 15281–15286.

102. Tian, Gang; Yang, Baozhong. Compactification of the moduli spaces of vortices and coupled vortices. J. Reine Angew. Math. 553 (2002), 17–41.

103. Cheeger, J.; Colding, T. H.; Tian, G. On the singularities of spaces with bounded Ricci curvature. Geom. Funct. Anal. 12 (2002), no. 5, 873–914.

104. Tian, Gang; Zhu, Xiaohua. A new holomorphic invariant and uniqueness of Kähler-Ricci solitons. Comment. Math. Helv. 77 (2002), no. 2, 297–325.

105. Tian, Gang. Constructing symplectic invariants. Quantum cohomology (Cetraro, 1997), 269–311, Lecture Notes in Math., 1776, Fond. CIME/CIME Found. Subser., Springer, Berlin, 2002.

106. Behrend, K.; Gómez, C.; Tarasov, V.; Tian, G. Quantum cohomology. Lectures given at the C.I.M.E. Summer School held in Cetraro, June 30–July 8, 1997. Edited by P. de Bartolomeis, B. Dubrovin and C. Reina. Lecture Notes in Mathematics, 1776. Fondazione CIME/CIME Foundation Subseries. Springer-Verlag, Berlin; Centro Internazionale Matematico Estivo (C.I.M.E.), Florence, 2002. viii+318 pp.

107. Chen, Jing Yi; Li, Jia Yu; Tian, Gang. Two-dimensional graphs moving by mean curvature flow. Acta Math. Sin. (Engl. Ser.) 18 (2002), no. 2, 209–224.

108. Tian, Gang. Extremal metrics and geometric stability. Special issue for S. S. Chern. Houston J. Math. 28 (2002), no. 2, 411–432.

109. Siebert, B.; Tian, Gang. Weierstrass polynomials and plane pseudo-holomorphic curves. Chinese Ann. Math. Ser. B 23 (2002), no. 1, 1–10.

110. Chen, X. X.; Tian, G. Ricci flow on Kähler-Einstein surfaces. Invent. Math. 147 (2002), no. 3, 487–544.

111. Tian, Gang. Symplectic isotopy in four dimension. First International Congress of Chinese Mathematicians (Beijing, 1998), 143–147, AMS/IP Stud. Adv. Math., 20, Amer. Math. Soc., Providence, RI, 2001.

112. Chen, Xiuxiong; Tian, Gang. Ricci flow on Kähler manifolds. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 3, 245–248.

113. Chen, Jingyi; Tian, Gang. Moving symplectic curves in Kähler-Einstein surfaces. Acta Math. Sin. (Engl. Ser.) 16 (2000), no. 4, 541–548.

114. Liu, Gang; Tian, Gang. Weinstein conjecture and GW-invariants. Commun. Contemp. Math. 2 (2000), no. 4, 405–459.

115. Tian, Gang. Canonical metrics in Kähler geometry. Notes taken by Meike Akveld. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 2000. vi+101 pp. 

116. Gao, Yi-hong; Tian, Gang. Instantons and the monopole-like equations in eight dimensions. J. High Energy Phys. 2000, no. 5, Paper 36, 23 pp.

117. Tian, Gang; Zhu, Xiaohua. Uniqueness of Kähler-Ricci solitons. Acta Math. 184 (2000), no. 2, 271–305.

118. Tian, Gang; Zhu, Xiaohua. A nonlinear inequality of Moser-Trudinger type. Calc. Var. Partial Differential Equations 10 (2000), no. 4, 349–354.

119. Li, Jiayu; Tian, Gang. The blow-up locus of heat flows for harmonic maps. Acta Math. Sin. (Engl. Ser.) 16 (2000), no. 1, 29–62.

120. Tian, Gang. Gauge theory and calibrated geometry. I. Ann. of Math. (2) 151 (2000), no. 1, 193–268.

121. Tian, Gang. Bott-Chern forms and geometric stability. Discrete Contin. Dynam. Systems 6 (2000), no. 1, 211–220.

122. Tian, Gang. Kähler-Einstein manifolds of positive scalar curvature. Surveys in differential geometry: essays on Einstein manifolds, 67–82, Surv. Differ. Geom., 6, Int. Press, Boston, MA, 1999.

123. Li, Jun; Tian, Gang. Comparison of algebraic and symplectic Gromov-Witten invariants. Asian J. Math. 3 (1999), no. 3, 689–728.

124. Li, Jun; Tian, Gang. A brief tour of GW invariants. Surveys in differential geometry: differential geometry inspired by string theory, 543–569, Surv. Differ. Geom., 5, Int. Press, Boston, MA, 1999.

125. Tian, Gang; Zhu, Xiaohua. Uniqueness of Kähler-Ricci solitons on compact Kähler manifolds. C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 11, 991–995.

126. Liu, Gang; Tian, Gang. On the equivalence of multiplicative structures in Floer homology and quantum homology. Acta Math. Sin. (Engl. Ser.) 15 (1999), no. 1, 53–80.

127. Siebert, Bernd; Tian, Gang. On hyperelliptic C∞-Lefschetz fibrations of four-manifolds. Commun. Contemp. Math. 1 (1999), no. 2, 255–280.

128. Chen, Jingyi; Tian, Gang. Compactification of moduli space of harmonic mappings. Comment. Math. Helv. 74 (1999), no. 2, 201–237.

129. Tian, Gang; Xin, Zhouping. Gradient estimation on Navier-Stokes equations. Comm. Anal. Geom. 7 (1999), no. 2, 221–257.

130. Liu, Xiaobo; Tian, Gang. Virasoro constraints for quantum cohomology. J. Differential Geom. 50 (1998), no. 3, 537–590.

131. Liu, Gang; Tian, Gang. Floer homology and Arnold conjecture. J. Differential Geom. 49 (1998), no. 1, 1–74.

132. Tian, Gang; Xin, Zhouping. One-point singular solutions to the Navier-Stokes equations. Topol. Methods Nonlinear Anal. 11 (1998), no. 1, 135–145.

133. Li, Jiayu; Tian, Gang. A blow-up formula for stationary harmonic maps. Internat. Math. Res. Notices 1998, no. 14, 735–755.

134. Li, Jun; Tian, Gang. Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds. Topics in symplectic 4-manifolds (Irvine, CA, 1996), 47–83, First Int. Press Lect. Ser., I, Int. Press, Cambridge, MA, 1998.

135. Li, Jun; Tian, Gang. Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties. J. Amer. Math. Soc. 11 (1998), no. 1, 119–174.

136. Siebert, Bernd; Tian, Gang. On quantum cohomology rings of Fano manifolds and a formula of Vafa and Intriligator. Asian J. Math. 1 (1997), no. 4, 679–695.

137. Li, Jun; Tian, Gang. Algebraic and symplectic geometry of Gromov-Witten invariants. Algebraic geometry—Santa Cruz 1995, 143–170, Proc. Sympos. Pure Math., 62, Part 2, Amer. Math. Soc., Providence, RI, 1997.

138. Li, Jun; Tian, Gang. The quantum cohomology of homogeneous varieties. J. Algebraic Geom. 6 (1997), no. 2, 269–305.

139. Ruan, Yongbin; Tian, Gang. Higher genus symplectic invariants and sigma models coupled with gravity. Invent. Math. 130 (1997), no. 3, 455–516.

140. Chen, J.; Tian, G. Minimal surfaces in Riemannian 4-manifolds. Geom. Funct. Anal. 7 (1997), no. 5, 873–916.

141. Tian, Gang. Kähler-Einstein metrics with positive scalar curvature. Invent. Math. 130 (1997), no. 1, 1–37.

142. Tian, Gang; Xu, Geng. On the semi-simplicity of the quantum cohomology algebras of complete intersections. Math. Res. Lett. 4 (1997), no. 4, 481–488.

143. Cheeger, Jeff; Colding, Tobias H.; Tian, Gang. Constraints on singularities under Ricci curvature bounds. C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), no. 6, 645–649.

144. Qing, Jie; Tian, Gang. Bubbling of the heat flows for harmonic maps from surfaces. Comm. Pure Appl. Math. 50 (1997), no. 4, 295–310.

145. Tian, Gang. Recent progress on Kähler-Einstein metrics. Geometry and physics (Aarhus, 1995), 149–155, Lecture Notes in Pure and Appl. Math., 184, Dekker, New York, 1997.

146. Tian, Gang. Kähler-Einstein metrics on algebraic manifolds. Transcendental methods in algebraic geometry (Cetraro, 1994), 143–185, Lecture Notes in Math., 1646, Fond. CIME/CIME Found. Subser., Springer, Berlin, 1996.

147. Demailly, J.-P.; Peternell, T.; Tian, G.; Tyurin, A. N. Transcendental methods in algebraic geometry. Lectures given at the 3rd C.I.M.E. Session held in Cetraro, July 4–12, 1994. Edited by F. Catanese and C. Ciliberto. Lecture Notes in Mathematics, 1646. Fondazione CIME/CIME Foundation Subseries. Springer-Verlag, Berlin; Centro Internazionale Matematico Estivo (C.I.M.E.), Florence, 1996. viii+247 pp.

148. De Bartolomeis, Paolo; Tian, Gang. Stability of complex vector bundles. J. Differential Geom. 43 (1996), no. 2, 231–275.

149. Lu, P.; Tian, G. The complex structures on connected sums of $S^3×S^3$. Manifolds and geometry (Pisa, 1993), 284–293, Sympos. Math., XXXVI, Cambridge Univ. Press, Cambridge, 1996.

150. Ruan, Yongbin; Tian, Gang. Higher genus symplectic invariants and sigma model coupled with gravity. Turkish J. Math. 20 (1996), no. 1, 75–83.

151. Ding, Weiyue; Tian, Gang. Energy identity for a class of approximate harmonic maps from surfaces. Comm. Anal. Geom. 3 (1995), no. 3-4, 543–554.

152. Ruan, Yongbin; Tian, Gang. A mathematical theory of quantum cohomology. J. Differential Geom. 42 (1995), no. 2, 259–367.

153. Siebert, Bernd; Tian, Gang. Recursive relations for the cohomology ring of moduli spaces of stable bundles. Turkish J. Math. 19 (1995), no. 2, 131–144.

154. Ruan, Yongbin; Tian, Gang. Bott-type symplectic Floer cohomology and its multiplication structures. Math. Res. Lett. 2 (1995), no. 2, 203–219.

155. Li, Peter; Tian, Gang. On the heat kernel of the Bergmann metric on algebraic varieties. J. Amer. Math. Soc. 8 (1995), no. 4, 857–877.

156. Tian, Gang. Quantum cohomology and its associativity. Current developments in mathematics, 1995 (Cambridge, MA), 361–401, Int. Press, Cambridge, MA, 1994.

157. Tian, Gang. The K-energy on hypersurfaces and stability. Comm. Anal. Geom. 2 (1994), no. 2, 239–265.

158. Cheeger, Jeff; Tian, Gang. On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay. Invent. Math. 118 (1994), no. 3, 493–571.

159. Stern, R.; Tian, Gang. Donaldson and Yau receive Crafoord prize. Notices Amer. Math. Soc. 41 (1994), no. 7, 794–796.

160. Lu, P.; Tian, G. The complex structure on a connected sum of $S^3×S^3$ with trivial canonical bundle. Math. Ann. 298 (1994), no. 4, 761–764.

161. Ruan, Yongbin; Tian, Gang. A mathematical theory of quantum cohomology. Math. Res. Lett. 1 (1994), no. 2, 269–278.

162. Li, Yan Yan; Tian, Gang. Harmonic maps with prescribed singularities. Differential geometry: partial differential equations on manifolds (Los Angeles, CA, 1990), 317–326, Proc. Sympos. Pure Math., 54, Part 1, Amer. Math. Soc., Providence, RI, 1993.

163. Tian, Gang. Degeneration of Kähler-Einstein manifolds. I. Differential geometry: geometry in mathematical physics and related topics (Los Angeles, CA, 1990), 595–609, Proc. Sympos. Pure Math., 54, Part 2, Amer. Math. Soc., Providence, RI, 1993.

164. Tian, Gang. Smoothing 3-folds with trivial canonical bundle and ordinary double points. Essays on mirror manifolds, 458–479, Int. Press, Hong Kong, 1992.

165. Ding, Wei Yue; Tian, Gang. Kähler-Einstein metrics and the generalized Futaki invariant. Invent. Math. 110 (1992), no. 2, 315–335.

166. Li, Yan Yan; Tian, Gang. Regularity of harmonic maps with prescribed singularities. Comm. Math. Phys. 149 (1992), no. 1, 1–30.

167. Tian, Gang. On stability of the tangent bundles of Fano varieties. Internat. J. Math. 3 (1992), no. 3, 401–413.

168. Tian, Gang. Compactness theorems for Kähler-Einstein manifolds of dimension 3 and up. J. Differential Geom. 35 (1992), no. 3, 535–558.

169. Luo, Feng; Tian, Gang. Liouville equation and spherical convex polytopes. Proc. Amer. Math. Soc. 116 (1992), no. 4, 1119–1129.

170. Tian, Gang. Some notes on Kähler-Einstein metrics with positive scalar curvature. Chinese mathematics into the 21st century (Tianjin, 1988), 67–83, Peking Univ. Press, Beijing, 1991.

171. Tian, Gang. Kähler-Einstein metrics on algebraic manifolds. Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 587–598, Math. Soc. Japan, Tokyo, 1991.

172. Tian, Gang. On one of Calabi's problems. Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989), 543–556, Proc. Sympos. Pure Math., 52, Part 2, Amer. Math. Soc., Providence, RI, 1991.

173. Li, Yan Yan; Tian, Gang. Nonexistence of axially symmetric, stationary solution of Einstein vacuum equation with disconnected symmetric event horizon. Manuscripta Math. 73 (1991), no. 1, 83–89.

174. Tian, Gang; Yau, Shing-Tung. Complete Kähler manifolds with zero Ricci curvature. II. Invent. Math. 106 (1991), no. 1, 27–60.

175. Tian, Gang. On a set of polarized Kähler metrics on algebraic manifolds. J. Differential Geom. 32 (1990), no. 1, 99–130.

176. Tian, G. On Calabi's conjecture for complex surfaces with positive first Chern class. Invent. Math. 101 (1990), no. 1, 101–172.

177. Tian, G.; Yau, Shing-Tung. Complete Kähler manifolds with zero Ricci curvature. I. J. Amer. Math. Soc. 3 (1990), no. 3, 579–609.

178. Tian, Gang. A Harnack type inequality for certain complex Monge-Ampère equations. J. Differential Geom. 29 (1989), no. 3, 481–488.

179. Tian, Gang. Kahler metrics on algebraic manifolds. Thesis (Ph.D.)–Harvard University. 1988.

180. Tian, Gang. On the existence of solutions of a class of Monge-Ampère equations. A Chinese summary appears in Acta Math. Sinica 32 (1989), no. 4, 576. Acta Math. Sinica (N.S.) 4 (1988), no. 3, 250–265.

181. Tian, Gang. Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Petersson-Weil metric. Mathematical aspects of string theory (San Diego, Calif., 1986), 629–646, Adv. Ser. Math. Phys., 1, World Sci. Publishing, Singapore, 1987.

182. Tian, G.; Yau, S.-T. Existence of Kähler-Einstein metrics on complete Kähler manifolds and their applications to algebraic geometry. Mathematical aspects of string theory (San Diego, Calif., 1986), 574–628, Adv. Ser. Math. Phys., 1, World Sci. Publishing, Singapore, 1987.

183. Tian, G.; Yau, S.-T. Three-dimensional algebraic manifolds with $C_1=0$ and $\chi=−6$. Mathematical aspects of string theory (San Diego, Calif., 1986), 543–559, Adv. Ser. Math. Phys., 1, World Sci. Publishing, Singapore, 1987.

184. Tian, Gang; Yau, Shing-Tung. Kähler-Einstein metrics on complex surfaces with $C_1>0$. Comm. Math. Phys. 112 (1987), no. 1, 175–203.

185. Tian, Gang. On Kähler-Einstein metrics on certain Kähler manifolds with $C_1(M)>0$. Invent. Math. 89 (1987), no. 2, 225–246.

186. Tian, Gang. On the mountain-pass lemma. Kexue Tongbao (English Ed.) 29 (1984), no. 9, 1150–1154.

187. Tian, Gang. On the mountain pass lemma. (Chinese) Kexue Tongbao (Chinese) 28 (1983), no. 14, 833–835.


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