2021/09/08 by Magdalena Caballero, Caballero, Magdalena
Mathematics · #35J93 #53C42 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2109.03686
openalex publication_date 2021/09/08 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
It is well known that the only surfaces that are simultaneously minimal in\n\ℝ3 and maximal in mathbbL3 are open pieces of helicoids (in\nthe region in which they are spacelike) and of spacelike planes (O. Kobayashi\n1983). The proof of this result consists in showing that the level curves of\nthose surfaces are lines, and so the surfaces are ruled. And it finishes\ncomparing the classification of minimal ruled surfaces to that of maximal ruled\nsurfaces.\n In this manuscript we consider the general case of spacelike hypersurfaces in\nthe (n+1)-dimensional Euclidean space which are simultaneously maximal and\nminimal. We show that its level curves are minimal hypersurfaces in the\nn-dimensional Euclidean space.\n