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Gradient Estimates for Harmonic Functions on Manifolds With Lipschitz Metrics

Published online by Cambridge University Press:  20 November 2018

Jingyi Chen  and
Elton P. Hsu
Jingyi Chen
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A.
Elton P. Hsu
Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60208, U.S.A. email: elton@math.nwu.edu
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Abstract

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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.

Keywords

60D5828D05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 6 , 01 December 1998 , pp. 1163 - 1175
Copyright
Copyright © Canadian Mathematical Society 1998

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