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Journal of Convex Analysis 12 (2005), No. 1, 139--143
Copyright Heldermann Verlag 2005

On Brickman's Theorem

Juan Enrique Martínez-Legaz
CODE and Departament d'Economica i d'Historia Economica, Universitat Autonoma de Barcelona, 08193 Bellaterra, Spain

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 R2 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

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