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Inventiones mathematicae

, Volume 99, Issue 1, pp 579–600 | Cite as

On the structure of complete Kähler manifolds with nonnegative curvature near infinity

  • Peter Li
Article

Keywords

Manifold Nonnegative Curvature 
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References

  1. [A-C-M] Avilés, P., Choi, H.I., Micallef, M.: The Dirichlet problem and Fatou's theorem for harmonic maps (Preprint)Google Scholar
  2. [B] Bando, S.: On the classification of three-dimensional compact Kaehler manifolds of nonnegative bisectional curvature. J. Differ. Geom.19, 283–297 (1984)Google Scholar
  3. [C-G] Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature. Ann. Math.92, 413–443 (1972)Google Scholar
  4. [C-C-L] Chen, C.H., Cheng, S.Y., Look, K.H.: On the Schwarz lemma for complete Kähler manifolds. Sci. Sin.22, 1238–1247 (1979)Google Scholar
  5. [C-L] Cheng, S.Y., Li, P.: Heat kernel estimates and lower bound of eigenvalues. Comment. Math. Helv.56, 327–338 (1981)Google Scholar
  6. [C] Croke, C.: Some isoperimetric inequalities and consequences. Ann. Sci. Ec. Norm. Super. 4, T13, 419–435 (1980)Google Scholar
  7. [D-L] Donnelly, H., Li, P.: Lower bounds for the eigenvalues of Riemannian manifolds. Mich. Math. J.29, 149–161 (1982)Google Scholar
  8. [G-W] Greene, R.E., Wu, H.:C approximations of convex subharmonic, and plurisubharmonic functions. Ann. Sci. Ec. Norm. Super. 4, T12, 47–84 (1979)Google Scholar
  9. [H] Hamilton, R.: Harmonic maps of manifolds with boundary. Lect. Notes Math., vol. 471, Berlin Heidelberg New York: Springer 1975Google Scholar
  10. [Ha] Hartman, P.: On homotopic harmonic maps. Can. J. Math.19, 673–687 (1967)Google Scholar
  11. [Hu] Huber, A.: On subharmonic functions and differential geometry in the large. Comment. Math. Helv.32, 13–72 (1957)Google Scholar
  12. [L] Li, P.: On the Sobolev constant and thep-spectrum of a compact Riemannian manifold. Ann. Sci. Ec. Norm. Super. 4, T13, 451–469 (1980)Google Scholar
  13. [L-T1] Li, P., Tam, L.F.: Positive harmonic functions on complete manifolds with nonnegative curvature outside a compact set. Ann. Math.125, 171–207 (1987)Google Scholar
  14. [L-T2] Li, P., Tam, L.F.: Symmetric Green's functions on complete manifolds. Am. J. Math.109, 1129–1154 (1987)Google Scholar
  15. [L-Y] Li, P., Yau, S.T.: Curvature and holomorphic mappings of complete Kähler manifolds. Compos. Math. (to appear)Google Scholar
  16. [Lu] Lu, Y.C.: Holomorphic mappings of complex manifolds. J. Differ. Geom.2, 299–312 (1968)Google Scholar
  17. [M] Mori, S.: Projective manifolds with ample tangent bundles. Ann. Math.110, 593–606 (1979)Google Scholar
  18. [Mo] Mok, N.: Compact Kähler manifolds of nonnegative holomorphic bisectional curvature. In: Grauert. U. (ed.) Complex analysis and algebraic geometry: Proc. Conf. Göttingen 1985 (Lect. Notes Math. vol. 1194, pp. 90–103) Berlin Heidelberg New York: Springer 1986Google Scholar
  19. [Sa] Sampson, J.H.: Applications of harmonic maps to Kähler geometry. Contemp. Math. (to appear)Google Scholar
  20. [S-Y] Schoen, R., Yau, S.T.: Harmonic maps and the topology of stable hypersurfaces and manifolds with nonnegative Ricci Curvature. Comment. Math. Helv.51, 333–341 (1976)Google Scholar
  21. [Si-Y] Siu, Y.T., Yau, S.T.: Compact Kähler manifolds of positive bisectional curvature. Invent. Math.59, 189–204 (1980)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Peter Li
    • 1
  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA

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