
Journal of Convex Analysis 12 (2005), No. 1, 139143 Copyright Heldermann Verlag 2005 On Brickman's Theorem Juan Enrique MartínezLegaz CODE and Departament d'Economica i d'Historia Economica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Spain JuanEnrique.Martinez@uab.es We give an elementary proof of a theorem of Brickman, which establishes the convexity of the image of the unit sphere of a space with dimension at least three under a vector mapping into R^{2} whose component functions are quadratic forms. We also discuss some consequences of this theorem regarding the range of that mapping. Keywords: Quadratic forms, convexity. MSC: 15A63, 52A10 [ Fulltextpdf (190 KB)] for subscribers only. 