Minimizing Neumann fundamental tones of triangles: an optimal Poincare inequality release_rev_1ec99882-8541-4a71-9265-1f26b89720a9

by R. Laugesen, B. Siudeja

Released as a article .

2009  

Abstract

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.
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Type  article
Stage   submitted
Date   2009-07-09
Version   v1
Language   en ?
arXiv  0907.1552v1
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