Local gradient estimate for harmonic functions on Finsler manifolds

Chao Xia

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Submission date: 18. Feb. 2014
Pages: 19
published in: Calculus of variations and partial differential equations, 51 (2014) 3/4, p. 849-865 
DOI number (of the published article): 10.1007/s00526-013-0697-2
Bibtex
MSC-Numbers: 31B05, 58B20, 35J15
Keywords and phrases: Finsler manifold, harmonic function, gradient estimate
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Abstract:
In this paper, we prove the local gradient estimate for harmonic functions on complete, noncompact Finsler measure spaces under the condition that the weighted Ricci curvature has a lower bound. As applications, we obtain Liouville type theorems on noncompact Finsler manifolds with nonnegative Ricci curvature.