Rigidity of Closed Convex Hypersurfaces in Multidimensional Spaces of Constant Curvature
In 1972, E.P. Sen'kin generalized the celebrated theorem of A.V. Pogorelov on the unique determination of closed convex surfaces by their intrinsic metrics in the Euclidean three-dimensional space $E^3$ to higher dimensional Euclidean spaces $E^{n+1}$ under a mild assumption on the smoothness o...
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1105 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | In 1972, E.P. Sen'kin generalized the celebrated theorem of A.V. Pogorelov on the unique determination of closed convex surfaces by their intrinsic metrics in the Euclidean three-dimensional space $E^3$ to higher dimensional Euclidean spaces $E^{n+1}$ under a mild assumption on the smoothness of hypersurfaces. In this paper, we remove that assumption and thereby establish a rigidity result for arbitrary closed convex hypersurfaces in $E^{n+1}$, $n \ge 3$. We also prove similar results in other model spaces of constant curvature.
Mathematical Subject Classification 2020: 52A10, 52A55, 51M10, 53C22 |
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