Steklov Eigenvalues of Submanifolds with Prescribed Boundary in Euclidean Space View Full Text


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Article Info

DATE

2019-04

AUTHORS

Bruno Colbois, Alexandre Girouard, Katie Gittins

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. More... »

PAGES

1-24

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12220-018-0063-x

DOI

http://dx.doi.org/10.1007/s12220-018-0063-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1105734046


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