Scalar curvature rigidity of warped product metrics
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911844297342976 |
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| author | Baer, Christian Brendle, Simon Hanke, Bernhard Wang, Yipeng |
| author_facet | Baer, Christian Brendle, Simon Hanke, Bernhard Wang, Yipeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_04015 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scalar curvature rigidity of warped product metrics Baer, Christian Brendle, Simon Hanke, Bernhard Wang, Yipeng Differential Geometry 53C20, 53C21, 53C27 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. |
| title | Scalar curvature rigidity of warped product metrics |
| topic | Differential Geometry 53C20, 53C21, 53C27 |
| url | https://arxiv.org/abs/2306.04015 |