Eigenvalues of Laplacians on a Closed Riemannian Manifold and Its Nets
Koji Fujiwara · Proceedings of the American Mathematical Society · 1995
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.