Steklov Eigenvalues of Submanifolds with Prescribed Boundary in Euclidean Space
Author(s)
Date issued
April 4, 2019
In
The Journal of Geometric Analysis
Vol
2
No
29
From page
1811
To page
1834
Reviewed by peer
1
Subjects
Steklov problem Euclidean space prescribed boundary manifolds hypersurfaces of revolution
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 Steklov isospectral to the disk.
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 Steklov isospectral to the disk.
Project(s)
Publication type
journal article
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