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Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index

Colbois, Bruno; Gittins, Katie

Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index Thumbnail


Authors

Bruno Colbois



Abstract

We obtain upper bounds for the Steklov eigenvalues σk(M)of a smooth, compact, n-dimensional submanifold M of Euclidean space with boundary Σ that involve the intersection indices of M and of Σ. One of our main results is an explicit upper bound in terms of the intersection index of Σ, the volume of Σand the volume of M as well as dimensional constants. By also taking the injectivity radius of Σinto account, we obtain an upper bound that has the optimal exponent of k with respect to the asymptotics of the Steklov eigenvalues as k→∞

Journal Article Type Article
Acceptance Date May 17, 2021
Online Publication Date Jul 29, 2021
Publication Date 2021-10
Deposit Date Jul 30, 2021
Publicly Available Date Jul 30, 2021
Journal Differential Geometry and its Applications
Print ISSN 0926-2245
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 78
Article Number 101777
DOI https://doi.org/10.1016/j.difgeo.2021.101777
Public URL https://durham-repository.worktribe.com/output/1269345

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