Minimizing Neumann fundamental tones of triangles: An optimal Poincaré inequality

R. S. Laugesen, B. A. Siudeja

Research output: Contribution to journalArticlepeer-review


The first nonzero eigenvalue of the Neumann Laplacian is shown to be minimal for the degenerate acute isosceles triangle, among all triangles of given diameter. Hence an optimal Poincaré inequality for triangles is derived.The proof relies on symmetry of the Neumann fundamental mode for isosceles triangles with aperture less than π/3. Antisymmetry is proved for apertures greater than π/3 copy; 2010 Elsevier Inc.

Original languageEnglish (US)
Pages (from-to)118-135
Number of pages18
JournalJournal of Differential Equations
Issue number1
StatePublished - Jul 2010


  • Free membrane
  • Isodiametric
  • Isoperimetric
  • Poincaré inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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