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

Colbois, Bruno and Gittins, Katie (2021) 'Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index.', Differential geometry and its applications., 78 . p. 101777.

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→∞

Item Type:Article
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Available under License - Creative Commons Attribution Non-commercial No Derivatives 4.0.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.difgeo.2021.101777
Publisher statement:© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Date accepted:17 May 2021
Date deposited:30 July 2021
Date of first online publication:29 July 2021
Date first made open access:30 July 2021

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