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arXiv · 1202.5108

Upper bounds for Steklov eigenvalues on surfaces

Alexandre Girouard·Iosif Polterovich
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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.

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Alexandre Girouard, Iosif Polterovich. 2012-02-23. Upper bounds for Steklov eigenvalues on surfaces. https://arxiv.org/abs/1202.5108

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