Local rigidity of convex hypersurfaces in spaces of constant curvature

2025/05/24 by Alexander A. Borisenko, Borisenko, Alexander A.
Mathematics · #51M10 #52A10 #52A55 #53C22 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2505.18564

openalex publication_date 2025/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a local rigidity of convex hypersurfaces in the spaces of constant curvature of dimension n≥4. 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 C¹-smoothness of the hypersurfaces.

Citations

• Rigidity of convex hypersurfaces, Rigidity of convex hypersurfaces in multidimensional spaces of constant curvature

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