Mathematische Annalen

, Volume 327, Issue 2, pp 339–349

The Bergman metric on complete Kähler manifolds


DOI: 10.1007/s00208-003-0456-3

Cite this article as:
Chen, BY. Math. Ann. (2003) 327: 339. doi:10.1007/s00208-003-0456-3


We use the existence of a bounded uniformly Hölder continuous plurisubharmonic exhaustion function to characterize the Bergman completeness of a complete Kähler manifold. As an application, we proved that any simply-connected complete Kähler manifold with sectional curvature bounded above by a negative constant is Bergman complete.

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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of Applied MathematicsTongji UniversityShanghaiP.R. China
  2. 2.Graduate School of MathematicsNagoya UniversityChikusa-kuJapan