Upper bounds for Steklov eigenvalues on surfaces

Details Upper bounds for Steklov eigenvalues on surfaces Upper bounds for Steklov eigenvalues on surfaces

2012-02-23

arxiv.org/abs/1202.5108v1

Mathematics

Spectral Theory

Scientific paper

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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