Spectral Gap of The Discrete Laplacian On Triangulations
arXiv:1907.05619 · doi:10.1063/1.5115778
Abstract
Our goal in this paper is to find an estimate for the spectral gap of the Laplacian on a 2-simplicial complex consisting on a triangulation of a complete graph. An upper estimate is given by generalizing the Cheeger constant. The lower estimate is obtained from the first non-zero eigenvalue of the discrete Laplacian acting on the functions of certain sub-graphs.