Some Liouville-type theorems for harmonic functions on Finsler manifolds |
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Authors: | Fu-e Zhang Qiaoling Xia |
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Institution: | 1. Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang Province, 310027, PR China;2. Department of Mathematics, Shihezi University, Shihezi 832003, PR China |
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Abstract: | In this paper, we give some Liouville-type theorems for Lp(p∈R) harmonic (resp. subharmonic, superharmonic) functions on forward complete Finsler manifolds. Moreover, we derive a gradient estimate for harmonic functions on a closed Finsler manifold. As an application, one obtains that any harmonic function on a closed Finsler manifold with nonnegative weighted Ricci curvature RicN(N∈(n,∞)) must be constant. |
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Keywords: | Finsler Laplacian Liouville-type theorem Harmonic function |
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