Gradient estimates for harmonic functions on manifolds with Lipschitz metrics

Jingyi Chen; Elton P Hsu

Gradient estimates for harmonic functions on manifolds with Lipschitz metrics

Jingyi Chen, Elton P Hsu

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We introduce a distributional Ricci curvature on complete smooth manifolds with Lipschitz continuous metrics. Under an assumption on the volume growth of geodesics balls, we obtain a gradient estimate for weakly harmonic functions if the distributional Ricci curvature is bounded below.

Original language	English
Pages (from-to)	1163
Journal	Canadian Journal of Mathematics
Volume	50
State	Published - 1998

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title = "Gradient estimates for harmonic functions on manifolds with Lipschitz metrics",

abstract = "We introduce a distributional Ricci curvature on complete smooth manifolds with Lipschitz continuous metrics. Under an assumption on the volume growth of geodesics balls, we obtain a gradient estimate for weakly harmonic functions if the distributional Ricci curvature is bounded below.",

author = "Jingyi Chen and Hsu, {Elton P}",

year = "1998",

language = "English",

volume = "50",

pages = "1163",

journal = "Canadian Journal of Mathematics",

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T1 - Gradient estimates for harmonic functions on manifolds with Lipschitz metrics

AU - Chen, Jingyi

AU - Hsu, Elton P

PY - 1998

Y1 - 1998

N2 - We introduce a distributional Ricci curvature on complete smooth manifolds with Lipschitz continuous metrics. Under an assumption on the volume growth of geodesics balls, we obtain a gradient estimate for weakly harmonic functions if the distributional Ricci curvature is bounded below.

AB - We introduce a distributional Ricci curvature on complete smooth manifolds with Lipschitz continuous metrics. Under an assumption on the volume growth of geodesics balls, we obtain a gradient estimate for weakly harmonic functions if the distributional Ricci curvature is bounded below.

M3 - Article

VL - 50

SP - 1163

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

ER -

Gradient estimates for harmonic functions on manifolds with Lipschitz metrics

Abstract

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