Dimension-like functions and spectrums of Finsler manifolds

Zhongmin Shen; Wei Zhao

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arXiv · 1806.04215

Dimension-like functions and spectrums of Finsler manifolds

Zhongmin Shen·Wei Zhao

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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.

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BibTeX RIS

Zhongmin Shen, Wei Zhao. 2018-06-11. Dimension-like functions and spectrums of Finsler manifolds. https://arxiv.org/abs/1806.04215

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