Dirichlet eigenvalue sums on triangles are minimal for equilaterals

Richard S Laugesen, Bartłomiej Andrzej Siudeja

Research output: Contribution to journalArticle

Abstract

Among all triangles of given diameter, the equilateral triangle is shown to minimize the sum of the first n eigenvalues of the Dirichlet Laplacian, for each n ≥ 1. In addition, the first, second and third eigenvalues are each proved to be minimal for the equilateral triangle. The disk is conjectured to be the minimizer among general domains.

Original languageEnglish (US)
Pages (from-to)855-885
Number of pages31
JournalCommunications in Analysis and Geometry
Volume19
Issue number5
StatePublished - Dec 1 2011

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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