Local rigidity of convex hypersurfaces in spaces of constant curvature

Fuente: arXiv
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Main Author: Borisenko, Alexander A.
Format: Preprint
Published: 2025
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author Borisenko, Alexander A.
author_facet Borisenko, Alexander A.
contents 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 convex isometric 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_18564
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Local rigidity of convex hypersurfaces in spaces of constant curvature
Borisenko, Alexander A.
Differential Geometry
52A10, 52A55, 51M10, 53C22
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 convex isometric 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.
title Local rigidity of convex hypersurfaces in spaces of constant curvature
topic Differential Geometry
52A10, 52A55, 51M10, 53C22
url https://arxiv.org/abs/2505.18564