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arXiv:1301.2222 [math.AP]AbstractReferencesReviewsResources

A graph discretization of the Laplace-Beltrami operator

Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev

Published 2013-01-10, updated 2014-11-09Version 4

We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.

Comments: 29 pages, v4: final, to appear in J of Spectral Theory
Categories: math.AP, math.DG, math.SP
Subjects: 58J50, 58J60, 65N25, 53C21, 05C50
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