Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (4): 1162-1172.doi: 10.1016/S0252-9602(17)30064-4

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ON THE FIRST EIGENVALUE OF THE MEAN FINSLER-LAPLACIAN

Qun HE1, Fanqi ZENG1, Daxiao ZENG2   

  1. 1. Schoolof Mathematical Sciences, Tongji University, Shanghai 200092, China;
    2. Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241002, China
  • Received:2015-03-19 Revised:2015-09-23 Online:2017-08-25 Published:2017-08-25
  • About author:Qun HE,E-mail:hequn@tongji.edu.cn;Fanqi ZENG,fanzeng10@126.com;Daxiao ZENG,E-mail:15556358915@163.com
  • Supported by:

    Project supported by NSFC (11471246) and NSFAP (1608085MA03).

Abstract:

In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry.

Key words: Finsler-Laplacian, mean metric, mean Laplacian, first eigenvalue

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