A note on eigenvalue bounds for non-compact manifolds
- In this article we prove upper bounds for the Laplace eigenvalues lambda(k) below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in terms of k(2) and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to -infinity, 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.
Author details: | Matthias KellerORCiDGND, Shiping Liu, Norbert PeyerimhoffORCiDGND |
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DOI: | https://doi.org/10.1002/mana.201900209 |
ISSN: | 0025-584X |
ISSN: | 1522-2616 |
Title of parent work (English): | Mathematische Nachrichten |
Publisher: | Wiley-VCH |
Place of publishing: | Weinheim |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/04/10 |
Publication year: | 2021 |
Release date: | 2024/05/29 |
Tag: | Cheeger inequality; Laplacian; Riemannian manifold; eigenvalues; negative curvature |
Volume: | 294 |
Issue: | 6 |
Number of pages: | 6 |
First page: | 1134 |
Last Page: | 1139 |
Funding institution: | Deutsche ForschungsgemeinschaftGerman Research Foundation (DFG) |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |
License (German): | CC-BY-NC-ND - Namensnennung, nicht kommerziell, keine Bearbeitungen 4.0 International |