Epigraphical Cones I

Up to orthogonal transformation, a solid closed convex cone K in the Euclidean space

is the epigraph of a nonnegative sublinear function f from

\mathbb{R}^n R n

to

\mathbb{R} 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.