Upper bounds for Steklov eigenvalues on surfaces
classification
🧮 math.SP
math.DG
keywords
boundaryboundseigenvaluessteklovupperapproachclassicalcompact
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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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