文献类型：期刊文献

英文题名：Nonlinear spectrums of Finsler manifolds

作者：Kristaly, Alexandru[1,2];Shen, Zhongmin[3];Yuan, Lixia[4];Zhao, Wei[5]

机构：[1]Babes Bolyai Univ, Dept Econ, Cluj Napoca 400591, Romania;[2]Obuda Univ, Inst Appl Math, H-1034 Budapest, Hungary;[3]Indiana Univ Purdue Univ, Dept Math Sci, Indianapolis, IN 46202 USA;[4]Shanghai Normal Univ, Sch Math & Phys, Shanghai 200234, Peoples R China;[5]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2022

卷号：300

期号：1

起止页码：81

外文期刊名：MATHEMATISCHE ZEITSCHRIFT

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000655937300001)】；

基金：The research of A. Kristaly is supported by the National Research, Development and Innovation Fund of Hungary, financed under the K_18 funding scheme, Project No. 127926. This work is also supported by theNationalNatural Science Foundation of China (No. 11501202, No. 11761058, No. 11671352, No. 12071423), the Natural Science Foundation of Shanghai (No. 17ZR1420900, No. 19ZR1411700) and the grant of China Scholarship Council (No. 201706745006). Work initiated whileW. Zhao was a visiting scholar at IUPUI. The authors would like to thank the Referee for her/his useful comments which improve the final presentation of the manuscript.

语种：英文

外文关键词：Eigenvalue; Eigenfunction; Finsler manifold; Sobolev space; Lusternik-Schnirelmann category; Krasnoselskii genus; Essential dimension; Lebesgue covering dimension

摘要：In this paper we investigate the spectral problem in Finsler geometry. Due to the nonlinearity of the Finsler-Laplacian operator, we introduce faithful dimension pairs by means of which the spectrum of a compact reversible Finsler metric measure manifold is defined. Various upper and lower bounds of such eigenvalues are provided in the spirit of Cheng, Buser and Gromov, which extend in several aspects the results of Hassannezhad, Kokarev and Polterovich. Moreover, we construct several faithful dimension pairs based on Lusternik-Schnirelmann category, Krasnoselskii genus and essential dimension, respectively; however, we also show that the Lebesgue covering dimension pair is not faithful. As an application, we show that the Bakry-emery spectrum of a closed weighted Riemannian manifold can be characterized by the faithful Lusternik-Schnirelmann dimension pair.