Upper bounds for Steklov eigenvalues on surfaces
Spectral Theory
2013-10-10 v1 Differential Geometry
Abstract
We give explicit isoperimetric upper bounds for all Steklov eigenvalues of a compact orientable surface with boundary, in terms of the genus, the length of the boundary, and the number of boundary components. Our estimates generalize a recent result of Fraser-Schoen, as well as the classical inequalites obtained by Hersch-Payne-Schiffer, whose approach is used in the present paper.
Cite
@article{arxiv.1202.5108,
title = {Upper bounds for Steklov eigenvalues on surfaces},
author = {Alexandre Girouard and Iosif Polterovich},
journal= {arXiv preprint arXiv:1202.5108},
year = {2013}
}