Local Rigidity of Convex Hypersurfaces in Spaces of Constant Curvature
In this paper, we prove a local rigidity of convex hypersurfaces in the spaces of constant curvature of dimension $n\ge4$. Namely, we show that two isometric convex hypersurfaces are congruent locally around their corresponding under the isometry points of strict convexity. This result extends the r...
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| Date: | 2026 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2026
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1122 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | In this paper, we prove a local rigidity of convex hypersurfaces in the spaces of constant curvature of dimension $n\ge4$. Namely, we show that two isometric convex hypersurfaces are congruent locally around their corresponding under the isometry points of strict convexity. This result extends the result of E.P. Senkin, who showed such rigidity under the additional assumption of $C^1$-smoothness of the hypersurfaces.
Mathematical Subject Classification 2020: 52A10, 52A55, 51M10, 53C22 |
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