Local rigidity of convex hypersurfaces in spaces of constant curvature

Abstract

In this paper, we prove a local rigidity of convex hypersurfaces in the spaces of constant curvature of dimension $n\ge 4$. 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 $C^1$-smoothness of the hypersurfaces.