Minimal roughness property of the Delaunay triangulation
Computer Aided Geometric Design
Robust 3D Shape Correspondence in the Spectral Domain
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
A Discrete Laplace–Beltrami Operator for Simplicial Surfaces
Discrete & Computational Geometry
A Monotonicity Property for Weighted Delaunay Triangulations
Discrete & Computational Geometry
Discrete laplace operator on meshed surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
A spectral characterization of the Delaunay triangulation
Computer Aided Geometric Design
Discrete heat kernel determines discrete Riemannian metric
Graphical Models
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The P1 discretization of the Laplace operator on a triangulated polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the P1 discretization of the Laplace operator. Among all triangles, an equilateral triangle has the maximal first positive eigenvalue. Among all cyclic quadrilaterals, a square has the maximal first positive eigenvalue. Among all cyclic n-gons, a regular one has the minimal value of the sum of all positive eigenvalues and the minimal value of the product of all positive eigenvalues.