Articles

ON THE FIRST EIGENVALUE OF THE MEAN FINSLER-LAPLACIAN

  • Qun HE ,
  • Fanqi ZENG ,
  • Daxiao ZENG
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  • 1. Schoolof Mathematical Sciences, Tongji University, Shanghai 200092, China;
    2. Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241002, China
Qun HE,E-mail:hequn@tongji.edu.cn;Fanqi ZENG,fanzeng10@126.com;Daxiao ZENG,E-mail:15556358915@163.com

Received date: 2015-03-19

  Revised date: 2015-09-23

  Online published: 2017-08-25

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.

Cite this article

Qun HE , Fanqi ZENG , Daxiao ZENG . ON THE FIRST EIGENVALUE OF THE MEAN FINSLER-LAPLACIAN[J]. Acta mathematica scientia, Series B, 2017 , 37(4) : 1162 -1172 . DOI: 10.1016/S0252-9602(17)30064-4

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