Hölder estimates and regularity for holomorphic and harmonic functions

Peter Li, Jiaping Wang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we proved that if a singular manifold satisfies a weak mean value property for positive subharmonic functions then one can derive an oscillation bound for bounded holomorphic functions. Moreover, if we further assume that the volume decays at most polynomially at a singular point, then we obtain a Hölder estimate of the holomorphic function at that point. In a similar spirit, we also established a continuity estimate for bounded harmonic functions, with a finite dimensional exception, at a singular point of a manifold satisfying a weak mean value property and a polynolmial volume decay condition.

Original languageEnglish (US)
Pages (from-to)309-329
Number of pages21
JournalJournal of Differential Geometry
Volume58
Issue number2
DOIs
StatePublished - 2001

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