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تسجيل مستخدم جديدDimension-like functions and spectrums of Finsler manifolds
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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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