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- Title
A note on eigenvalue bounds for non-compact manifolds.
- Authors
Keller, Matthias; Shiping Liu; Peyerimhoff, Norbert
- Abstract
In this article we prove upper bounds for the Laplace eigenvalues λk below the essential spectrum for strictly negatively curved Cartan–Hadamard manifolds. Our bound is given in terms of k² and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to −∞, where no essential spectrum is present due to a theorem of Donnelly/Li. The result stands in clear contrast to Laplacians on graphs where such a bound fails to be true in general
- Subjects
EIGENVALUES; CURVATURE
- Publication
Mathematische Nachrichten, 2021, Vol 294, Issue 6, p1134
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.201900209