## Complete Kähler manifolds with zero Ricci curvature. I

HTML articles powered by AMS MathViewer

- by G. Tian and Shing-Tung Yau PDF
- J. Amer. Math. Soc.
**3**(1990), 579-609 Request permission

## References

- Richard L. Bishop and Richard J. Crittenden,
*Geometry of manifolds*, Pure and Applied Mathematics, Vol. XV, Academic Press, New York-London, 1964. MR**0169148** - 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**, DOI 10.1007/978-3-642-96754-2 - S. Y. Cheng and S.-T. Yau,
*Inequality between Chern numbers of singular Kähler surfaces and characterization of orbit space of discrete group of $\textrm {SU}(2,1)$*, 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**, DOI 10.1090/conm/049/833802 - David Gilbarg and Neil S. Trudinger,
*Elliptic partial differential equations of second order*, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin-New York, 1977. MR**0473443**, DOI 10.1007/978-3-642-96379-7 - 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**, DOI 10.1007/BFb0063413 - Robin Hartshorne,
*Ample vector bundles*, Inst. Hautes Études Sci. Publ. Math.**29**(1966), 63–94. MR**193092** - 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** - J. Milnor,
*A note on curvature and fundamental group*, J. Differential Geometry**2**(1968), 1–7. MR**232311**, DOI 10.4310/jdg/1214501132 - 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**437797**, DOI 10.2307/1970998 - 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** - H. Wu,
*Manifolds of partially positive curvature*, Indiana Univ. Math. J.**36**(1987), no. 3, 525–548. MR**905609**, DOI 10.1512/iumj.1987.36.36029 - 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**397619**, DOI 10.24033/asens.1299 - 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**, DOI 10.1002/cpa.3160310304 - Shing Tung Yau,
*A general Schwarz lemma for Kähler manifolds*, Amer. J. Math.**100**(1978), no. 1, 197–203. MR**486659**, DOI 10.2307/2373880

## Additional Information

- © Copyright 1990 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**3**(1990), 579-609 - MSC: Primary 53C55; Secondary 32C10, 53C25
- DOI: https://doi.org/10.1090/S0894-0347-1990-1040196-6
- MathSciNet review: 1040196