Extremum problems for eigenvalues of discrete Laplace operators

Details Extremum problems for eigenvalues of discrete Laplace operators Extremum problems for eigenvalues of discrete Laplace operators

2011-06-29

arxiv.org/abs/1106.5844v1

Mathematics

Metric Geometry

12 pages

Scientific paper

The discrete Laplace operator on a triangulated polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the discrete Laplace operators. Among all triangles, an equilateral triangle has the maximal first positive eigenvalue. Among all cyclic quadrilateral, 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 nontrivial eigenvalues and the minimal value of the product of all nontrivial eigenvalues.

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