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.

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References in corpus (5)

• Simplicial Quantum Gravity
• Random Delaunay triangulations, the Thurston-Andreev theorem, and metric uniformization
• 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

Cited by in corpus (15)

• Discrete Quasi-Einstein Metrics and Combinatorial Curvature Flows in 3-Dimension
• On the deformation of inversive distance circle packings, II
• Simplicial Ricci Flow
• A combinatorial Yamabe problem on two and three dimensional manifolds
• On the deformation of ball packings
• A new proof of Bowers-Stephenson conjecture
• Combinatorial Calabi flows on surfaces
• Topological Signals of Singularities in Ricci Flow
• Rigidity of discrete conformal structures on surfaces
• Alexandrov's theorem, weighted Delaunay triangulations, and mixed volumes
• On the global rigidity of sphere packings on 3-dimensional manifolds
• Discrete conformal variations and scalar curvature on piecewise flat two and three dimensional manifolds
• Regge's Einstein-Hilbert Functional on the Double Tetrahedron
• Fractional combinatorial Calabi flow on surfaces
• Equivalence of Simplicial Ricci Flow and Hamilton's Ricci Flow for 3D Neckpinch Geometries