On Gromov's rigidity theorem for polytopes with acute angles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909676129484800 |
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| author | Brendle, S. Wang, Y. |
| author_facet | Brendle, S. Wang, Y. |
| contents | In his ``Four Lectures", Gromov conjectured a scalar curvature extremality property of convex polytopes. Moreover, Gromov outlined a proof of the conjecture in the special case when the dihedral angles are acute. Gromov's argument relies on Dirac operator techniques together with a smoothing construction. In this paper, we give the details of such a smoothing construction, thereby providing a detailed proof of Gromov's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08000 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Gromov's rigidity theorem for polytopes with acute angles Brendle, S. Wang, Y. Differential Geometry In his ``Four Lectures", Gromov conjectured a scalar curvature extremality property of convex polytopes. Moreover, Gromov outlined a proof of the conjecture in the special case when the dihedral angles are acute. Gromov's argument relies on Dirac operator techniques together with a smoothing construction. In this paper, we give the details of such a smoothing construction, thereby providing a detailed proof of Gromov's theorem. |
| title | On Gromov's rigidity theorem for polytopes with acute angles |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2308.08000 |