
Journal of Convex Analysis 30 (2023), No. 4, 12031216 Copyright Heldermann Verlag 2023 On the Gauss Range of a Closed Convex Set Juan Enrique MartínezLegaz Dep. d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, Barcelona Graduate School of Mathematics, Spain JuanEnrique.Martinez.Legaz@uab.es Cornel Pintea Faculty of Mathematics and Computer Science, BabesBolyai University, ClujNapoca, Romania, Romania cpintea@math.ubbcluj.ro The aim of this paper is twofold. One one hand we study how the Gauss range of a closed convex subset of the Euclidean space changes when acting on the given set with an affine automorphism. On the other hand we investigate the sphericalconvexity of the Gauss range of such a set. Since the Gauss range is not always sphericallyconvex, we focus our attention on the sphericalconvexity of its spherical interior and of its closure as well. Examples of closed convex sets with sphericallyconvex Gauss ranges are, among others, the epigraphs of suitable lower semicontinuous convex functions. Keywords: Closed convex set, Gauss range, sphericallyconvex set. MSC: 52A20, 26B25. [ Fulltextpdf (138 KB)] for subscribers only. 