2022/06/02 by Stéphane Simon, Simon, Stéphane, Patrick Verovic +1
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Optimization and Variational Analysis #Point processes and geometric inequalities #math.FA
paper · pdf · doi:10.48550/arxiv.2206.01016
arxiv created 2022/06/02 · openalex publication_date 2022/06/02 · arxiv updated 2022/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to give two complete and simple characterizations of Minkowski norms N on an arbitrary topological real vector space such that the sublevel sets of N are strictly convex. We first show that this property is equivalent to the continuity of N together with the fact that any open chord between two points of the boundary of the sublevel set N-1([0, 1)) lies inside that set (geometric characterization). On the other hand, we prove that this is also the same as saying that N is continuous and that for an arbitrary real number α > 1 the function N^α is strictly convex (analytic characterization).