Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
839670 | Nonlinear Analysis: Theory, Methods & Applications | 2015 | 11 Pages |
Abstract
Let (M,F)(M,F) be an nn-dimensional compact Finsler manifold without boundary or with a convex boundary and λ1λ1 be the first (nonzero) closed or Neumann eigenvalue of the Finsler Laplacian on MM with nonnegative weighted Ricci curvature. In this paper, we prove that λ1≥π2d2, where dd is the diameter of MM, and that the equality holds if and only if MM is a 11-dimensional circle or a 11-dimensional segment, which generalize the well-known Zhong–Yang’s sharp estimate in Riemannian geometry (Zhong and Yang, 1984).
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Authors
Qiaoling Xia,