On the first eigenvalue of Finsler manifolds with nonnegative weighted Ricci curvature  

作　　者：YIN SongTing HE Qun SHEN YiBing 

机构地区：[1]Department of Mathematics,Tongji University [2]Department of Mathematics and Computer Science,Tongling University [3]Department of Mathematics,Zhejiang University

出　　处：《Science China Mathematics》2014年第5期1057-1070,共14页中国科学：数学（英文版）

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)

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.

关 键 词：Finsler-Laplacian the first eigenvalue Ricci curvature S curvature 

分 类 号：O186.1[理学—数学]