Local gradient estimate for harmonic functions on Finsler manifolds

Article, Preprint English OPEN
Xia, Chao (2013)
  • Journal: Calculus of variations and partial dierential equations (issn: 0944-2669)
  • Related identifiers: doi: 10.1007/s00526-013-0697-2
  • Subject: Mathematics - Analysis of PDEs | Mathematics - Differential Geometry
    arxiv: Mathematics::Differential Geometry | Mathematics::Metric Geometry | Mathematics::Symplectic Geometry

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 theorem on Finsler manifolds with nonnegative Ricci curvature.
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