Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 

 

Complete Kähler manifolds with zero Ricci curvature. I


Authors: G. Tian and Shing-Tung Yau
Journal: J. Amer. Math. Soc. 3 (1990), 579-609
MSC: Primary 53C55; Secondary 32C10, 53C25
MathSciNet review: 1040196
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [Bi] Richard L. Bishop and Richard J. Crittenden, Geometry of manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York-London, 1964. MR 0169148
  • [BPV] W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574
  • [CY] S. Y. Cheng and S.-T. Yau, Inequality between Chern numbers of singular Kähler surfaces and characterization of orbit space of discrete group of 𝑆𝑈(2,1), Complex differential geometry and nonlinear differential equations (Brunswick, Maine, 1984) Contemp. Math., vol. 49, Amer. Math. Soc., Providence, RI, 1986, pp. 31–44. MR 833802, 10.1090/conm/049/833802
  • [GT] David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin-New York, 1977. Grundlehren der Mathematischen Wissenschaften, Vol. 224. MR 0473443
  • [GW] R. E. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Mathematics, vol. 699, Springer, Berlin, 1979. MR 521983
  • [Ha] Robin Hartshorne, Ample vector bundles, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 63–94. MR 0193092
  • [Jo] Jürgen Jost, Harmonic mappings between Riemannian manifolds, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 4, Australian National University, Centre for Mathematical Analysis, Canberra, 1984. MR 756629
  • [Mi] J. Milnor, A note on curvature and fundamental group, J. Differential Geometry 2 (1968), 1–7. MR 0232311
  • [SY] Yum Tong Siu and Shing Tung Yau, Complete Kähler manifolds with nonpositive curvature of faster than quadratic decay, Ann. of Math. (2) 105 (1977), no. 2, 225–264. MR 0437797
  • [TY] G. Tian and S.-T. Yau, Existence of Kähler-Einstein metrics on complete Kähler manifolds and their applications to algebraic geometry, Mathematical aspects of string theory (San Diego, Calif., 1986) Adv. Ser. Math. Phys., vol. 1, World Sci. Publishing, Singapore, 1987, pp. 574–628. MR 915840
  • [Wu] H. Wu, Manifolds of partially positive curvature, Indiana Univ. Math. J. 36 (1987), no. 3, 525–548. MR 905609, 10.1512/iumj.1987.36.36029
  • [Y1] Shing Tung Yau, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Sci. École Norm. Sup. (4) 8 (1975), no. 4, 487–507. MR 0397619
  • [Y2] Shing Tung Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math. 31 (1978), no. 3, 339–411. MR 480350, 10.1002/cpa.3160310304
  • [Y3] Shing Tung Yau, A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100 (1978), no. 1, 197–203. MR 0486659

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC: 53C55, 32C10, 53C25

Retrieve articles in all journals with MSC: 53C55, 32C10, 53C25


Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1990-1040196-6
Article copyright: © Copyright 1990 American Mathematical Society