
Journal of Convex Analysis 31 (2024), No. 1, 139178 Copyright Heldermann Verlag 2024 When is a Minkowski Norm Strictly SubConvex? Stéphane Simon Université Savoie Mont Blanc, CNRS, LAMA, Chambéry, France Stephane.Simon@univsmb.fr Patrick Verovic Université Savoie Mont Blanc, CNRS, LAMA, Chambéry, France Patrick.Verovic@univsmb.fr 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). Keywords: Minkowski norms, affine geometry, quasiconvexity, gauge functions, topological vector spaces, strict subconvexity. MSC: 52A07; 52A05. [ Fulltextpdf (243 KB)] for subscribers only. 