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Journal of Convex Analysis 18 (2011), No. 4, 1171--1196
Copyright Heldermann Verlag 2011

Epigraphical Cones I

Alberto Seeger
University of Avignon, Dept. of Mathematics, 33 rue Louis Pasteur, 84000 Avignon, France

Up to orthogonal transformation, a solid closed convex cone K in the Euclidean space Rn+1 is the epigraph of a nonnegative sublinear function f from Rn to R. This work explores the link between the geometric properties of K and the analytic properties of f. Part two of this article is published in this journal 19 (2012), Number 1.

Keywords: Convex cone, epigraphical cone, sublinear function, inradius of a cone, solidity, pointedness, angular spectrum.

MSC: 46B10, 46B20, 52A41

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