Geometric triangulations and discrete Laplacians on manifolds

Abstract

This paper uses the technology of weighted and regular triangulations to study discrete versions of the Laplacian on piecewise Euclidean manifolds. Regular triangulations are studied in some detail, including flip algorithms. The Laplacian is then studied as an operator on functions of the vertices as a generalized weighted Laplacian on graphs.

8 figures

References in corpus (3)

• An extended correction to ``Combinatorial Scalar Curvature and Rigidity of Ball Packings,'' (by D. Cooper and I. Rivin)
• Metrized graphs, electrical networks, and Fourier analysis
• Spectral Convergence of the Discrete Laplacian on Models of a Metrized Graph