关于芬斯勒可反系数的一个注记

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英文篇名：A Note on the Reversibility of Finsler Manifolds 作者：尹松庭 英文作者：Yin Songting;Department of Mathematics and Computer Science, Tongling University;Key Laboratory of Applied Mathematics(Putian University),Fujian Province University; 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 英文关键词：Finsler manifold;;Reversibility;;The first eigenvalue;;Comparison theorem;;Volume growth 中文刊名：SXWX 英文刊名：Acta Mathematica Scientia 机构：铜陵学院数学与计算机学院;应用数学福建省高校重点实验室(莆田学院); 出版日期：2019-06-15 出版单位：数学物理学报 年：2019 期：v.39 基金：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)~~ 语种：中文; 页：SXWX201903002 页数：8 CN：03 ISSN：42-1226/O 分类号：9-16

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.
        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.

引文

[1]Cheng S Y.Eigenvalue comparison theorems and its geometric applications.Math Z,1975,143(3):289-297
    [2]陈滨.芬斯勒几何中的若干分析问题[D].浙江:浙江大学,2010Chen B.Some geometric and analysis problems in Finsler geometry[D].Zhejiang:Zhejiang University,2010
    [3]Huang G Y,Li Z.Upper bounds on the first eigenvalue for the p-Laplacian.Anal Math Phys,DOI10.1007/sl3324-017-0168-6
    [4]Ohta S,Sturm K-T.Heat flow on Finsler manifolds.Comm Pure Appl Math,2009,62:1386-1433
    [5]Rademacher H B.A sphere theorem for non-reversible Finsler metrics.Math Ann,2004,328:373-387
    [6]Shen Z M.The Non-Linear Laplacian for finsler manifolds//Antonelli P.The Theory of Finslerian Laplacians and Applications.Netherlands:Kluwer Acad Press,1998
    [7]Wu B Y,Xin Y L.Comparison theorems in Finsler geometry and their applications.Math Ann,2007,337:177-196
    [8]Yin S T,He Q.Some comparison theorems and their applications in Finsler geometry.J Ineq Appl,2014,2014:107
    [9]Yin S T,He Q.Eigenvalue comparison theorems on Finsler manifolds.Chin Ann Math,2015,36B(1):31-44