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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Bibliographic Details
Date:2026
Main Author: Borisenko, Alexander A.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2026
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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
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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