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Gradient estimates for harmonic Functions on manifolds with Lipschitz metrics

Published:1998-12-01
Printed: Dec 1998
• Jingyi Chen
• Elton P. Hsu
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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.
 MSC Classifications: 60D58 - unknown classification 60D5828D05 - Measure-preserving transformations