English

Bounds on the multiplicity of eigenvalues for fixed membranes

Analysis of PDEs 2007-05-23 v3 Differential Geometry

Abstract

For a membrane in the plane the multiplicity of the kk-th eigenvalue is known to be not greater than 2k12k-1. Here we prove that it is actually not greater than 2k32k-3, for k3k\ge 3.

Cite

@article{arxiv.math/9801090,
  title  = {Bounds on the multiplicity of eigenvalues for fixed membranes},
  author = {Thomas Hoffman-Ostenhof and Peter W. Michor and Nikolai Nadirashvili},
  journal= {arXiv preprint arXiv:math/9801090},
  year   = {2007}
}

Comments

AmSTeX, epsf.tex, 17 encapsulated postscript figures, 17 pages. Third version with minor stylistic improvements

R2 v1 2026-07-22T17:57:30.264Z