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Steklov Eigenvalues of Submanifolds with Prescribed Boundary in Euclidean Space
Auteur(s)
Date de parution
2019-4-4
In
The Journal of Geometric Analysis
Vol.
2
No
29
De la page
1811
A la page
1834
Revu par les pairs
1
Résumé
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.
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Identifiants
Type de publication
journal article
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