数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (4): 1162-1172.doi: 10.1016/S0252-9602(17)30064-4

• 论文 • 上一篇    下一篇

ON THE FIRST EIGENVALUE OF THE MEAN FINSLER-LAPLACIAN

贺群1, 曾凡奇1, 郑大小2   

  1. 1. Schoolof Mathematical Sciences, Tongji University, Shanghai 200092, China;
    2. Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241002, China
  • 收稿日期:2015-03-19 修回日期:2015-09-23 出版日期:2017-08-25 发布日期:2017-08-25
  • 作者简介:Qun HE,E-mail:hequn@tongji.edu.cn;Fanqi ZENG,fanzeng10@126.com;Daxiao ZENG,E-mail:15556358915@163.com
  • 基金资助:

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

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).

摘要:

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.

关键词: Finsler-Laplacian, mean metric, mean Laplacian, first eigenvalue

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