2020/12/30 by Julián Haddad, Haddad, J., D. O. Silva +1
Mathematics · Physics and Astronomy · #53C24 #53C60 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2012.15206
openalex publication_date 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend to Minkowski spaces the classical result of Barbosa and do Carmo [1] that characterizes the euclidean sphere as the unique compact stable CMC hypersurface of \mathbb Rn. More precisely, if K is a smooth convex body in \mathbb Rn with positive Gauss curvature, containing the origin in its interior and M is an immersed hypersurface, there are well defined concepts of surface area measure, normal vector field and principal curvatures of M , with respect to K. Thus, we introduce the concept of stability with respect to normal variations and compute the formula of second variation with respect to K. Finally we show that if M is compact, has constant mean Minkowski curvature and is stable (with respect to K) then M is homothetic to ∂ K.