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

In 1972, E. P. Senkin generalized the celebrated theorem of A. V. Pogorelov on unique determination of compact convex surfaces by their intrinsic metrics in the Euclidean 3-space E³ to higher dimensional Euclidean spaces Eⁿ⁺¹ under a mild assumption on the smoothness of the hypersurface. In this paper, we remove this assumption and thus establish this rigidity result for arbitrary compact, convex hypersurfaces in Eⁿ⁺¹, n ≥ 3. We also prove the corresponding results in other model spaces of constant curvature.