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Eigenvalues of Laplacians on a closed Riemannian manifold and its nets


Author: Koji Fujiwara
Journal: Proc. Amer. Math. Soc. 123 (1995), 2585-2594
MSC: Primary 58G25; Secondary 58G99
MathSciNet review: 1257106
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Abstract: We show that the eigenvalues of the Laplacian of a closed manifold M is approximated in a certain sense by the eigenvalues of the Laplacian of the graph of a $ \frac{1}{n}$-net in M as $ n \to \infty $. Our approximation needs no assumption on M except for dimension.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1257106-5
Article copyright: © Copyright 1995 American Mathematical Society