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.
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→∞
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|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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