Three-circle theorem and dimension estimate for holomorphic functions on Kähler manifolds

Gang Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

The classical Hadamard three-circle theorem is generalized to complete Kähler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three-circle theorem. Two sharp monotonicity formulae are derived as corollaries. Among applications, we obtain sharp dimension estimates (with rigidity) of holomorphic functions with polynomial growth when the holomorphic sectional curvature is nonnegative. When the bisectional curvature is nonnegative, the sharp dimension estimate was due to Ni.

Original languageEnglish (US)
Pages (from-to)2899-2919
Number of pages21
JournalDuke Mathematical Journal
Volume165
Issue number15
DOIs
StatePublished - 2016

ASJC Scopus subject areas

  • Mathematics(all)

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