2022/03/19 by Hilário Alencar, Alencar, Hilário, Márcio Batista +3
Mathematics · #35J15 #35J60 #53E10 #58J05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Primary: 53C21 #Secondary: 53C42
paper · pdf · doi:10.48550/arxiv.2203.10334
openalex publication_date 2022/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, under mild constraints on the sectional curvature, we exploit a divergence formula for symmetric endomorphisms to deduce a general Poincaré type inequality. We apply such inequality to higher-order mean curvature of hypersurfaces of space forms and Einstein manifolds, to obtain several isoperimetric inequalities, as well as rigidity results for complete r-minimal hypersurfaces satisfying a suitable decay of the second fundamental form at infinity. Furthermore, using these techniques, we prove flatness and non-existence results for self-similar solutions to a large class of fully nonlinear curvature flows.