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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
18/2014

Local gradient estimate for harmonic functions on Finsler manifolds

Chao Xia

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.

Received:
Feb 18, 2014
Published:
Feb 25, 2014
MSC Codes:
31B05, 58B20, 35J15
Keywords:
Finsler manifold, harmonic function, gradient estimate

Related publications

inJournal
2014 Repository Open Access
Chao Xia

Local gradient estimate for harmonic functions on Finsler manifolds

In: Calculus of variations and partial differential equations, 51 (2014) 3/4, pp. 849-865