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 |
|---|---|
| Full text: | (VoR) Version of Record Available under License - Creative Commons Attribution Non-commercial No Derivatives 4.0. Download PDF (437Kb) |
| 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 |
Save or Share this output
| Export: | |
| Look up in GoogleScholar |
