Eigenvalues of Laplacians on a closed Riemannian manifold and its nets

Fujiwara, Koji

doi:10.1090/S0002-9939-1995-1257106-5

Eigenvalues of Laplacians on a closed Riemannian manifold and its nets
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Proc. Amer. Math. Soc. 123 (1995), 2585-2594 Request permission

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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