Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces
Differential Geometry
2013-11-26 v3 Spectral Theory
Abstract
We prove two explicit bounds for the multiplicities of Steklov eigenvalues on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the index of an eigenvalue, while the other depends as well on the number of boundary components. We also show that on any given smooth Riemannian surface with boundary, the multiplicities of Steklov eigenvalues are uniformly bounded in .
Keywords
Cite
@article{arxiv.1209.4869,
title = {Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces},
author = {Mikhail Karpukhin and Gerasim Kokarev and Iosif Polterovich},
journal= {arXiv preprint arXiv:1209.4869},
year = {2013}
}
Comments
final version, 17 pages, to appear in Annales de l'Institut Fourier