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Journal Article

Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space

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Gittins,  Katie
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s12220-018-0063-x
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Citation

Colbois, B., Girouard, A., & Gittins, K. (2019). Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space. Journal of Geometric Analysis, 29(2), 1811-1834. doi:10.1007/s12220-018-0063-x.


Cite as: https://hdl.handle.net/21.11116/0000-0004-40C0-A
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.