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Gradient estimates for harmonic Functions on manifolds with Lipschitz metrics |
Canad. J. Math. 50(1998), 1163-1175
Published:1998-12-01
Printed: Dec 1998
Printed: Dec 1998
- Jingyi Chen
- Elton P. Hsu
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 60D58 28D05 - Measure-preserving transformations |