Bruno Colbois
Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index
Colbois, Bruno; Gittins, Katie
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→∞
Citation
Colbois, B., & Gittins, K. (2021). Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index. Differential Geometry and its Applications, 78, Article 101777. https://doi.org/10.1016/j.difgeo.2021.101777
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 |
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Copyright 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/).
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