On the volume growth of kähler manifolds with nonnegative bisectional curvature

Gang Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let M be a complete Kahler manifold with nonnegative bisectional curvature. Suppose the universal cover does not split and M admits a nonconstant holomorphic function with polynomial growth; we prove M must be of maximal volume growth. This confirms a conjecture of Ni in [17]. There are two essential ingredients in the proof: the Cheeger Colding theory [2] [5] on Gromov Hausdorff convergence of manifolds and the three circle theorem for holomorphic functions in [14].

Original languageEnglish (US)
Pages (from-to)485-500
Number of pages16
JournalJournal of Differential Geometry
Volume102
Issue number3
DOIs
StatePublished - Mar 2016

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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