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Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces

Mikhail Karpukhin; Gerasim Kokarev; Iosif Polterovich — 2014

Annales de l’institut Fourier

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 Riemannian surface with smooth boundary the multiplicities of Steklov eigenvalues $σ_{k}$ are uniformly bounded in $k$ .

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