Upper bounds for Steklov eigenvalues on surfaces

By A. Girouard, Iosif Polterovich. 2012

54 citations recorded by the source corpus.

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.

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

View Paper: https://www.semanticscholar.org/paper/3105485b6dc7e89b326dc79b7a6753414786c68f

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In Applied Mathematics

1. M. Li
2. Marco A. M. Guaraco
3. Hung Tran
4. Xin Zhou
5. Antoine Song
6. Peter J. McGrath
7. Jusuf Ramic
8. Camillo De Lellis

In Computational Theory and Mathematics

1. M. Li
2. Marco A. M. Guaraco
3. Hung Tran
4. Jusuf Ramic
5. Xin Zhou
6. Camillo De Lellis

In Mathematical Physics

1. M. Li

Citations in the corpus

• Free boundary minimal surfaces in the unit ball : recent advances and open questions (2019, background): “ j-th Steklov eigenfunction corresponding to the j-th Steklov eigenvalue ˙ j. We now focus on the case that is a surface. By the work of Fraser and Schoen [24] (for k= 1) and Girouard and Polterovich [32] (for k2), we have the following coarse upper bound for the k-th Steklov eigenvalue only in term”
• SPECTRAL GEOMETRY OF THE STEKLOV PROBLEM (2014, unknown): “ for Steklov eigenvalues on surfaces. On a compact surface with boundary, the following theorem gives a general upper bound in terms of the genus and the number of boundary components. Theorem 4.2.1 ([44]). Let be a smooth orientable compact surface with boundary M= @ of length L. Let be the genus o”