Karpukhin, Mikhail;
(2017)
Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds.
Electronic Research Announcements in Mathematical Sciences
, 24
pp. 100-109.
10.3934/era.2017.24.011.
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Abstract
Consider a compact Riemannian manifold with boundary. In this short note we prove that under certain positive curvature assumptions on the manifold and its boundary the Steklov eigenvalues of the manifold are controlled by the Laplace eigenvalues of the boundary. Additionally, in two dimensions we obtain an upper bound for Steklov eigenvalues in terms of topology of the surface without any curvature restrictions.
| Type: | Article |
|---|---|
| Title: | Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.3934/era.2017.24.011 |
| Publisher version: | https://doi.org/10.3934/era.2017.24.011 |
| Language: | English |
| Additional information: | This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Steklov eigenvalues, geometric optimisation. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10201293 |
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