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Eigenvalues of elliptic operators and geometric applications

Alexander Grigoryan Yuri Netrusov Shing-Tung Yau

Differential Geometry mathscidoc:1912.43522

Surveys in differential geometry, 9, (1), 147-217, 2004
Eigenvalues and capacitors. Let X be a Riemannian manifold and be the Laplace operator on X. It is well-known that if X is compact then the spectrum of is discrete and consists of an increasing sequence {k} k= 1 of the eigenvalues (counted with the multiplicities) where 1= 0 and k as k. Moreover, if n= dim X then Weyls asymptotic formula says that (1.1) k cn
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@inproceedings{alexander2004eigenvalues,
  title={Eigenvalues of elliptic operators and geometric applications},
  author={Alexander Grigoryan, Yuri Netrusov, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203809645068086},
  booktitle={Surveys in differential geometry},
  volume={9},
  number={1},
  pages={147-217},
  year={2004},
}
Alexander Grigoryan, Yuri Netrusov, and Shing-Tung Yau. Eigenvalues of elliptic operators and geometric applications. 2004. Vol. 9. In Surveys in differential geometry. pp.147-217. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203809645068086.
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