Bounds on the multiplicity of eigenvalues for fixed membranes

1998/01/31 by Thomas Hoffman-Ostenhof, Peter W. Michor, Nikolai Nadirashvili · 2 citations
Mathematics · #math.AP #math.DG #msc:35B05 #msc:35P15 #msc:58G25

paper · pdf

published as Geometric And Functional Analysis (GAFA). Vol. 9 (1999), 1169-1188 · AmSTeX, epsf.tex, 17 encapsulated postscript figures, 17 pages. Third version with minor stylistic improvements

arxiv created 1999/06/02 · arxiv updated 2009/11/30

Abstract

For a membrane in the plane the multiplicity of the k-th eigenvalue is known to be not greater than 2k-1. Here we prove that it is actually not greater than 2k-3, for k≥ 3.

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