数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 423-430.

• 论文 • 上一篇    下一篇

关于芬斯勒可反系数的一个注记

尹松庭1,2()   

  1. 1 铜陵学院数学与计算机学院 安徽铜陵 244000
    2 应用数学福建省高校重点实验室(莆田学院) 福建莆田 351100
  • 收稿日期:2017-12-04 出版日期:2019-06-26 发布日期:2019-06-27
  • 作者简介:尹松庭, yst419@163.com
  • 基金资助:
    国家自然科学基金(11471246);安徽省自然科学基金(1608085MA03);铜陵学院人才科研启动基金项目(2015tlxyrc09);应用数学福建省高校重点实验室(莆田学院)开放课题(SX201805)

A Note on the Reversibility of Finsler Manifolds

Songting Yin1,2()   

  1. 1 Department of Mathematics and Computer Science, Tongling University, Anhui Tongling, 244000
    2 Key Laboratory of Applied Mathematics(Putian University), Fujian Province University, Fujian Putian 351100
  • Received:2017-12-04 Online:2019-06-26 Published:2019-06-27
  • Supported by:
    the NSFC(11471246);the AHNSF(1608085MA03);the TLXYRC(2015tlxyrc09);the KLAMFPU(SX201805)

摘要:

该文在加权Ricci曲率具有下界时给出了关于芬斯勒Laplacian第一特征值的郑绍远型及Mckean型比较定理,并在加权Ricci曲率非负时得到Calabi-Yau型体积增长定理.这改进和推广了已有的方法和结果.特别地,该文利用芬斯勒度量及其反向度量对应的几何对象之间的关系,去掉或减弱了可反系数有限的条件限制.

关键词: 芬斯勒流形, 可反系数, 第一特征值, 比较定理, 体积增长

Abstract:

For a Finsler manifold with the weighted Ricci curvature bounded from below, we give Cheng type and Mckean type comparison theorems for the first eigenvalue of Finsler Laplacian. When the weighted Ricci curvature is nonnegative, we also obtain Calabi-Yau type volume growth theorem. These generalize and improve some recent literatures. Especially, by using the relationship of the counterparts between a Finsler metric and its reverse metric, we remove some restrictions on the reversibility.

Key words: Finsler manifold, Reversibility, The first eigenvalue, Comparison theorem, Volume growth

中图分类号: 

  • O186