Rigidity of convex hypersurfaces, Rigidity of convex hypersurfaces in multidimensional spaces of constant curvature
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916297573400576 |
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| author | Borisenko, Alexander A. |
| author_facet | Borisenko, Alexander A. |
| contents | In 1972, E. P. Senkin generalized the celebrated theorem of A. V. Pogorelov on unique determination of compact convex surfaces by their intrinsic metrics in the Euclidean 3-space $E^3$ to higher dimensional Euclidean spaces $E^{n+1}$ under a mild assumption on the smoothness of the hypersurface. In this paper, we remove this assumption and thus establish this rigidity result for arbitrary compact, convex hypersurfaces in $E^{n+1}$, $n \ge 3$. We also prove the corresponding results in other model spaces of constant curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15761 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity of convex hypersurfaces, Rigidity of convex hypersurfaces in multidimensional spaces of constant curvature Borisenko, Alexander A. Differential Geometry 52A10, 52A55, 51M10, 53C22 In 1972, E. P. Senkin generalized the celebrated theorem of A. V. Pogorelov on unique determination of compact convex surfaces by their intrinsic metrics in the Euclidean 3-space $E^3$ to higher dimensional Euclidean spaces $E^{n+1}$ under a mild assumption on the smoothness of the hypersurface. In this paper, we remove this assumption and thus establish this rigidity result for arbitrary compact, convex hypersurfaces in $E^{n+1}$, $n \ge 3$. We also prove the corresponding results in other model spaces of constant curvature. |
| title | Rigidity of convex hypersurfaces, Rigidity of convex hypersurfaces in multidimensional spaces of constant curvature |
| topic | Differential Geometry 52A10, 52A55, 51M10, 53C22 |
| url | https://arxiv.org/abs/2406.15761 |