Maximizing Neumann fundamental tones of triangles

R. S. Laugesen, B. A. Siudeja

Research output: Contribution to journalArticlepeer-review


We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proven for the harmonic and arithmetic means of the first two nonzero eigenvalues.

Original languageEnglish (US)
Article number112903
JournalJournal of Mathematical Physics
Issue number11
StatePublished - 2009

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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