Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (4): 829-845.doi: 10.1016/S0252-9602(09)60073-4

• Articles • Previous Articles     Next Articles

POSITIVELY CURVED COMPLETE NONCOMPACT KÄHLER MANIFOLDS

 CHEN Bing-Long, SHU Xi-Beng   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • Received:2008-12-31 Online:2009-07-20 Published:2009-07-20
  • Supported by:

    This work was partially supported by 973 project (2006CB805905) and NSFC (10831008)

Abstract:

In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. Among other things, we prove that a complete noncompact K¨ahler surface with positive and bounded sectional curvature and with finite analytic Chern number c1(M)2 is biholomorphic to C2.

Key words: uniformization conjectures, compactification

CLC Number: 

  • 53C55
Trendmd