A graph discretization of the Laplace-Beltrami operator

Abstract

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.

29 pages, v4: final, to appear in J of Spectral Theory