Publications and preprints

Preprints

1. Futaki invariant and CM polarization, Gang Tian (Posted on June 18, 2015. Downloads:   )

2. Orbifold regularity of weak Kähler-Einstein metrics, Chi Li, Gang Tian (Posted on May 7, 2015. Downloads:   )

In this note, we prove that any non-collapsing and compact Gromov-Hausdorff limit of Kähler-Einstein manifolds is either smooth or is orbifold outside a subvariety of complex codimension at least 3.

3. Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type, Gang Tian, Zhenlei Zhang (Posted on May 7, 2015. Downloads:   )

In this paper, we prove that the $L^4$-norm of Ricci curvature is uniformly bounded along a Kähler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold M of general type and with dimension n < 4, any solution of the normalized Kähler-Ricci flow converges to the unique singular Kähler-Einstein metric on the canonical model of M in the Cheeger-Gromov topology.

4. Kähler-Einstein metrics on Fano manifolds, Gang Tian (Posted on December 5, 2014. Downloads:   )

This is an expository paper Kähler metrics of positive scalar curvature. It is for my Takagi lectures at RIMS in November of 2013. In this paper, I first discuss the Futaki invariants, the K-stability and its relation to the K-energy. Next I will outline my work in 2012 on the existence of Kähler-Einstein metrics on K-stable Fano manifolds. Finally, I will present S. Paul’s work on stability of pairs with some modifications of mine.

5. K-stability implies CM-stability, Gang Tian (Posted on September 28, 2014. Downloads:   )

In this paper, we prove that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper.

6. A third derivative estimate for conic Monge-Ampere equations, Gang Tian (Posted on February 28, 2014. Downloads:   )

We apply the arguments in my PKU Master degree thesis to derive a third derivative estimate, and consequently, a $C^{2\alpha}$-estimate, for complex Monge-Ampere equations in the conic case. A slightly weaker version already appeared as an appendix in the paper of Jeffres-Mazzeo-Rubinstein for constructing conic Kähler-Einstein metrics.

7. Regularity of Kähler-Ricci flows on Fano manifolds, Gang Tian, Zhenlei Zhang (Posted on October 23, 2013. Downloads:   )

 GT-20131023.pdf

8. K-stability and Kähler-Einstein metrics, Gang Tian (Posted on October 18, 2013. Updated on Aug 18, 2015. Downloads:   )

In October of 2012, I announced a proof for the existence of Kähler-Einstein metrics on K-stable Fano manifolds. In February of 2013, I submitted the paper which contains my proof. Based on referees’ reports I received, I improved the presentation, added more explanations and streamlined arguments in my proof. Also I removed some discussions not directly related to the proof even though they will be useful for future purpose. This updated version is based on my published version which can be found at http://onlinelibrary.wiley.com/doi/10.1002/cpa.v68.7/issuetoc

9. Stability of pairs, Gang Tian (Posted on October 18, 2013. Updated on Sept 23, 2014. Downloads:   )

This is an expository note based on S. Paul’s works on the stability of pairs ([Pa12a], [Pa12b], [Pa13], [Pa08]). Some revisions are made and typos are corrected.

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

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

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

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

5. 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.

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

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

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

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

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

11. 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.

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

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

14. 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.

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

16. Chen, Xiuxiong; Sun, Song; Tian, Gang A note on K\”ahler-Ricci soliton.
Int. Math. Res. Not. IMRN (2009), no. 17, 3328–3336.

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

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

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

20. 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.

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

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

23. 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.

24. 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.

25. Lu, Guangcun; Tian, Gang Constructing virtual Euler cycles and classes. Int. Math. Res. Surv. IMRS (2007), no. 1, 220 pp.

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

27. 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.

28. 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.

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

30. 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.

31. 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 (electronic).

32. 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.

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

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

35. Cao, Huai-Dong; Tian, Gang; Zhu, Xiaohua Kähler-Ricci solitons on compact complex manifolds with $C\sb 1(M)>0$. Geom. Funct. Anal. 15 (2005), no. 3, 697–719.

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

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

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

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

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

41. 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.

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

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

44. 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.

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

46. 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.

47. 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.

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

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

50. 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

51. 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.

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

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

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

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

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

57. 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.

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

59. Tian, Gang Constructing symplectic invariants. Quantum cohomology (Cetraro, 1997), 269–311, Lecture Notes in Math., 1776, Springer, Berlin, 2002.

60. 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 C.I.M.E.. [C.I.M.E. Foundation] Springer-Verlag, Berlin; Centro Internazionale Matematico Estivo (C.I.M.E.), Florence, 2002. viii+318 pp.

61. 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.

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

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

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

65. 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.

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

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

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

69. Tian, Gang Canonical metrics in Kähler geometry. Notes taken by Meike Akveld. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 2000. vi+101 pp. ISBN: 3-7643-6194-8

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

71. 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.

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

73. 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.

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

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

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

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

78. 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.

79. 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.

80. 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.

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

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

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

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

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

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

87. 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.

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

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

90. 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.

91. 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.

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

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

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

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

96. 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.

97. 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.

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

99. 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.

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

101. 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 C.I.M.E.. [C.I.M.E. Foundation] Springer-Verlag, Berlin; Centro Internazionale Matematico Estivo (C.I.M.E.), Florence, 1996. viii+247 pp.

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

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

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

105. 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.

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

107. 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.

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

109. 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.

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

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

122. 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.

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

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

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

126. 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.

127. 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.

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

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

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

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

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

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

134. 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.

135. 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.

136. 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.

137. 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.

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

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

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

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

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

143. 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.

144. 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.

145. 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.

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

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

148. Tian, Gang On Kähler-Einstein metrics on certain Kähler manifolds with $C\sb 1(M)>0$. Invent. Math. 89 (1987), no. 2, 225–246.

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

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

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