Scalar Curvature Rigidity of Warped Product Metrics
We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212160 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Scalar Curvature Rigidity of Warped Product Metrics. Christian Bär, Simon Brendle, Bernhard Hanke and Yipeng Wang. SIGMA 20 (2024), 035, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862657020876816384 |
|---|---|
| author | Bär, Christian Brendle, Simon Hanke, Bernhard Wang, Yipeng |
| author_facet | Bär, Christian Brendle, Simon Hanke, Bernhard Wang, Yipeng |
| citation_txt | Scalar Curvature Rigidity of Warped Product Metrics. Christian Bär, Simon Brendle, Bernhard Hanke and Yipeng Wang. SIGMA 20 (2024), 035, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round spheres of dimension at least 3 with two antipodal points removed. This resolves a problem in Gromov's ''Four Lectures'' in all dimensions. Our arguments are based on spin geometry.
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| first_indexed | 2026-03-15T21:44:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212160 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T21:44:31Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bär, Christian Brendle, Simon Hanke, Bernhard Wang, Yipeng 2026-01-30T08:14:04Z 2024 Scalar Curvature Rigidity of Warped Product Metrics. Christian Bär, Simon Brendle, Bernhard Hanke and Yipeng Wang. SIGMA 20 (2024), 035, 26 pages 1815-0659 2020 Mathematics Subject Classification: 53C20; 53C21; 53C27 arXiv:2306.04015 https://nasplib.isofts.kiev.ua/handle/123456789/212160 https://doi.org/10.3842/SIGMA.2024.035 We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round spheres of dimension at least 3 with two antipodal points removed. This resolves a problem in Gromov's ''Four Lectures'' in all dimensions. Our arguments are based on spin geometry. The first-named author was supported by DFG-SPP 2026 “Geometry at Infinity”. The second-named author was supported by the National Science Foundation under grant DMS-2103573 and by the Simons Foundation. The third-named author was supported by DFG-SPP 2026 “Geometry at Infinity” and by Columbia University. We would like to thank the anonymous referees for their insightful comments, which helped to improve the exposition. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Scalar Curvature Rigidity of Warped Product Metrics Article published earlier |
| spellingShingle | Scalar Curvature Rigidity of Warped Product Metrics Bär, Christian Brendle, Simon Hanke, Bernhard Wang, Yipeng |
| title | Scalar Curvature Rigidity of Warped Product Metrics |
| title_full | Scalar Curvature Rigidity of Warped Product Metrics |
| title_fullStr | Scalar Curvature Rigidity of Warped Product Metrics |
| title_full_unstemmed | Scalar Curvature Rigidity of Warped Product Metrics |
| title_short | Scalar Curvature Rigidity of Warped Product Metrics |
| title_sort | scalar curvature rigidity of warped product metrics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212160 |
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