scholarly journals Local gradient estimate for harmonic functions on Finsler manifolds

2013 ◽  
Vol 51 (3-4) ◽  
pp. 849-865 ◽  
Author(s):  
Chao Xia
Keyword(s):  
Harmonic Functions ◽  
Gradient Estimate ◽  
Finsler Manifolds ◽  
Local Gradient

Gradient Estimates for Harmonic Functions on Manifolds With Lipschitz Metrics

1998 ◽  
Vol 50 (6) ◽  
pp. 1163-1175 ◽  
Author(s):  
Jingyi Chen ◽  
Elton P. Hsu
Keyword(s):  
Ricci Curvature ◽  
Harmonic Functions ◽  
Volume Growth ◽  
Gradient Estimate ◽  
Gradient Estimates ◽  
Smooth Manifolds ◽  
Lipschitz Continuous ◽  
Bounded Below

AbstractWe 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.

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