TY - JOUR
T1 - Hölder estimates and regularity for holomorphic and harmonic functions
AU - Li, Peter
AU - Wang, Jiaping
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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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U2 - 10.4310/jdg/1090348328
DO - 10.4310/jdg/1090348328
M3 - Article
AN - SCOPUS:0035384547
SN - 0022-040X
VL - 58
SP - 309
EP - 329
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
IS - 2
ER -