Journal of Differential Geometry

Hölder Estimates and Regularity for Holomorphic and Harmonic Functions

Peter Li and Jiaping Wang

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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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J. Differential Geom., Volume 58, Number 2 (2001), 309-329.

First available in Project Euclid: 20 July 2004

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Li, Peter; Wang, Jiaping. Hölder Estimates and Regularity for Holomorphic and Harmonic Functions. J. Differential Geom. 58 (2001), no. 2, 309--329. doi:10.4310/jdg/1090348328.

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