Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds
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 these Steklov eigenvalues in terms of topology of the surface without any curvature restrictions.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2015
- DOI:
- 10.48550/arXiv.1512.09038
- arXiv:
- arXiv:1512.09038
- Bibcode:
- 2015arXiv151209038K
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Spectral Theory