Graph approximations to the Laplacian spectra
Jinpeng Lu · Journal of Topology and Analysis · 2019
I prove that the spectrum of the Laplace–Beltrami operator with the Neumann boundary condition on a compact Riemannian manifold with boundary admits a fast approximation by the spectra of suitable graph Laplacians on proximity graphs on the manifold, and similar graph approximation works for metric-measure spaces glued out of compact Riemannian manifolds of the same dimension.