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arXiv · 1209.4869

Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces

Mikhail Karpukhin·Gerasim Kokarev·Iosif Polterovich
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Abstract

We prove two explicit bounds for the multiplicities of Steklov eigenvalues $σ_k$ on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the index $k$ 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 $σ_k$ are uniformly bounded in $k$.

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Mikhail Karpukhin, Gerasim Kokarev, Iosif Polterovich. 2013-11-24. Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces. https://arxiv.org/abs/1209.4869

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