Open Access
June, 2001 Hölder Estimates and Regularity for Holomorphic and Harmonic Functions
Peter Li, Jiaping Wang
J. Differential Geom. 58(2): 309-329 (June, 2001). DOI: 10.4310/jdg/1090348328


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.


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Peter Li. Jiaping Wang. "Hölder Estimates and Regularity for Holomorphic and Harmonic Functions." J. Differential Geom. 58 (2) 309 - 329, June, 2001.


Published: June, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1049.58024
MathSciNet: MR1913945
Digital Object Identifier: 10.4310/jdg/1090348328

Rights: Copyright © 2001 Lehigh University

Vol.58 • No. 2 • June, 2001
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