文献类型：期刊文献

英文题名：Nonlinear spectrums of finsler manifolds

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

机构：[1] Department of Economics, Babe?-Bolyai University, Cluj-Napoca, 400591, Romania; [2] Institute of Applied Mathematics, Obuda University, Budapest, 1034, Hungary; [3] Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, IN, United States; [4] School of Mathematics and Physics, Shanghai Normal University, Shanghai, China; [5] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2019

外文期刊名：arXiv

收录：EI(收录号：20200388624)

语种：英文

外文关键词：Geometry - Sobolev spaces

摘要：In this paper, we study the spectral problem in Finsler geometry. The spectrum of a Finsler metric measure manifold is defined to be the set of the critical values of the canonical energy functional, which is captured by a faithful dimension-like function. We estimate both the upper bound and the lower bound of such eigenvalues. Moreover, several faithful dimension-like functions are constructed in this paper. As an application, we show the spectrum of a weighted Riemannian manifold can be obtained by a special faithful dimension-like function. Copyright ? 2019, The Authors. All rights reserved.