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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, 28D05 show english descriptions unknown classification 60D58
Measure-preserving transformations
60D58 - unknown classification 60D58
28D05 - Measure-preserving transformations
 

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