Total Mean Curvature and First Dirac Eigenvalue
In this note, we prove an optimal upper bound for the first Dirac eigenvalue of some hypersurfaces in the Euclidean space by combining a positive mass theorem and the construction of quasi-spherical metrics. As a direct consequence of this estimate, we obtain an asymptotic expansion for the first ei...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211914 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Total Mean Curvature and First Dirac Eigenvalue. Simon Raulot. SIGMA 19 (2023), 029, 14 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | In this note, we prove an optimal upper bound for the first Dirac eigenvalue of some hypersurfaces in the Euclidean space by combining a positive mass theorem and the construction of quasi-spherical metrics. As a direct consequence of this estimate, we obtain an asymptotic expansion for the first eigenvalue of the Dirac operator on large spheres in three-dimensional asymptotically flat manifolds. We also study this expansion for small geodesic spheres in a three-dimensional Riemannian manifold. We finally discuss how this method can be adapted to yield similar results in the hyperbolic space.
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| ISSN: | 1815-0659 |