@article{discovery1405894, title = {A graph discretization of the Laplace-Beltrami operator}, year = {2014}, number = {4}, journal = {Journal of Spectral Theory}, pages = {675--714}, note = {{\copyright} European Mathematical Society.}, publisher = {EUROPEAN MATHEMATICAL SOC}, month = {January}, volume = {4}, issn = {1664-039X}, author = {Burago, D and Ivanov, S and Kurylev, Y}, 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.}, url = {http://dx.doi.org/10.4171/JST/83}, keywords = {Laplace, graph, discretization, Riemannian, RIEMANNIAN-MANIFOLDS, CONVERGENCE} }