摘要
We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed(resp.Neumann)eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle(resp.a segment).Moreover,a lower bound of the first eigenvalue of Finsler-Laplacian with Dirichlet boundary condition is also estimated.These generalize the corresponding results in recent literature.
We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed（resp. Neumann） eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle（resp. a segment）. Moreover,a lower bound of the first eigenvalue of Finsler-Laplacian with Dirichlet boundary condition is also estimated. These generalize the corresponding results in recent literature.
基金
supported by National Natural Science Foundation of China(Grant No.11171253)
the Natural Science Foundation of Ministry of Education of Anhui Province(Grant No.KJ2012B197)
