Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces

By Mikhail A. Karpukhin, G. Kokarev, Iosif Polterovich. 2012

62 citations recorded by the source corpus.

We prove two explicit bounds for the multiplicities of Steklov eigenvalues $\sigma_k$ 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 $\sigma_k$ are uniformly bounded in $k$.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/906edea30de751ac1d0ee733d423a7d8c224b588

Citations in the corpus

• SPECTRAL GEOMETRY OF THE STEKLOV PROBLEM (2014, unknown): “Putting together the results of [70, 67, 66, 39] we get the following bounds:”