1. CJM 1998 (vol 50 pp. 1163)
|Gradient estimates for harmonic Functions on manifolds with Lipschitz metrics |
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.