Dimension-like functions and spectrums of Finsler manifolds

Zhongmin Shen; Wei Zhao

Dimension-like functions and spectrums of Finsler manifolds

Differential Geometry 2019-07-02 v3

Authors: Zhongmin Shen , Wei Zhao

Abstract

In this paper, we study the spectral problem on a compact Finsler manifold with or without boundary. More precisely, given a certain collection of sets in Sobolev space $H^{1,2}(M)$ and a dimension-like function, we can define a corresponding spectrum. Such a spectrum satisfies nice properties. In particular, the eigenfunction corresponding to each eigenvalue always exists. And a Cheng type upper bound estimate for eigenvalues is obtained. Moreover, some interesting examples are constructed and investigated in this paper.

Keywords

finsler manifold spectrum dimension-like function sobolev space eigenvalue estimate compact manifold

Cite

@article{arxiv.1806.04215,
  title  = {Dimension-like functions and spectrums of Finsler manifolds},
  author = {Zhongmin Shen and Wei Zhao},
  journal= {arXiv preprint arXiv:1806.04215},
  year   = {2019}
}

Comments

A new co-author joins in this work and helps to improve this paper. So this paper should be withdraw in order to exclude any confusion

Dimension-like functions and spectrums of Finsler manifolds

Abstract

Keywords

Cite

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