Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space
Spectral Theory
2018-01-22 v2 Differential Geometry
Abstract
We obtain upper and lower bounds for Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space. A very general upper bound is proved, which depends only on the geometry of the fixed boundary and on the measure of the interior. Sharp lower bounds are given for hypersurfaces of revolution with connected boundary: we prove that each eigenvalue is uniquely minimized by the ball. We also observe that each surface of revolution with connected boundary is isospectral to the disk.
Cite
@article{arxiv.1711.06458,
title = {Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space},
author = {Bruno Colbois and Alexandre Girouard and Katie Gittins},
journal= {arXiv preprint arXiv:1711.06458},
year = {2018}
}
Comments
24 pages, 2 figures