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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211914 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Total Mean Curvature and First Dirac Eigenvalue. Simon Raulot. SIGMA 19 (2023), 029, 14 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862652439717478400 |
|---|---|
| author | Raulot, Simon |
| author_facet | Raulot, Simon |
| citation_txt | Total Mean Curvature and First Dirac Eigenvalue. Simon Raulot. SIGMA 19 (2023), 029, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-15T16:18:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211914 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T16:18:28Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Raulot, Simon 2026-01-16T11:18:31Z 2023 Total Mean Curvature and First Dirac Eigenvalue. Simon Raulot. SIGMA 19 (2023), 029, 14 pages 1815-0659 2020 Mathematics Subject Classification: 53C27; 53C40; 53C80; 58G25 arXiv:2210.13037 https://nasplib.isofts.kiev.ua/handle/123456789/211914 https://doi.org/10.3842/SIGMA.2023.029 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Total Mean Curvature and First Dirac Eigenvalue Article published earlier |
| spellingShingle | Total Mean Curvature and First Dirac Eigenvalue Raulot, Simon |
| title | Total Mean Curvature and First Dirac Eigenvalue |
| title_full | Total Mean Curvature and First Dirac Eigenvalue |
| title_fullStr | Total Mean Curvature and First Dirac Eigenvalue |
| title_full_unstemmed | Total Mean Curvature and First Dirac Eigenvalue |
| title_short | Total Mean Curvature and First Dirac Eigenvalue |
| title_sort | total mean curvature and first dirac eigenvalue |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211914 |
| work_keys_str_mv | AT raulotsimon totalmeancurvatureandfirstdiraceigenvalue |