Local gradient estimate for harmonic functions on Finsler manifolds
type: Item
instance of: scholarly article
title: Local gradient estimate for harmonic functions on Finsler manifolds
zbMATH Open document ID: 1316.53083
author: Chao Xia
published in: Calculus of Variations and Partial Differential Equations
publication date: 2014-11-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1308.3609
review text: The study of harmonic functions is one of the central topics in geometric analysis, and in the Riemannian setting, a lot of interesting and important results have been obtained. The main goal of this paper is to generalize the local gradient estimate to Finsler manifolds. The author presents a local gradient estimate for harmonic functions on complete, noncompact Finsler measure spaces under the condition that the weighted Ricci curvature has a lower bound. This estimate is applied to obtain some Liouville-type theorems on noncompact Finsler manifolds with nonnegative Ricci curvature.
reviewed by: Shaoqiang Deng
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 6369378
zbMATH Keywords: local gradient estimate
zbMATH Keywords: Finsler measure spaces
zbMATH Keywords: weighted Ricci curvature
zbMATH Keywords: Liouville type theorems
MaRDI profile type: Publication
OpenAlex ID: W2151106741
arXiv ID: 1308.3609
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DOI: 10.1007/S00526-013-0697-2
description: scientific article; zbMATH DE number 6369378