2012/08/08 by Xu Cheng, Cheng, Xu, Detang Zhou +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1208.1786
openalex publication_date 2012/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Perez proved some L2 inequalities for closed convex hypersurfaces immersed in the Euclidean space ℝn+1, more generally, for closed hypersurfaces with non-negative Ricci curvature, immersed in an Einstein manifold. In this paper, we discuss the rigidity of these inequalities when the ambient manifold is ℝn+1, the hyperbolic space ℍn+1, or the closed hemisphere \mathbbS+n+1. We also obtain a generalization of the Perez's theorem to the hypersurfaces without the hypothesis of non-negative Ricci curvature.