Eigenvalues of Laplacians on a closed Riemannian manifold and its nets

作者：Koji Fujiwara · 发表于：Proceedings of the American Mathematical Society · 年份：1995 · DOI：10.1090/s0002-9939-1995-1257106-5 · 被引用次数：85 · 研究领域：Spectral Theory in Mathematical Physics、Advanced Mathematical Modeling in Engineering、Nonlinear Partial Differential Equations

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 1 n \frac {1}{n} -net in M as n → ∞ n \to \infty . Our approximation needs no assumption on M except for dimension.