Epigraphical Cones I

Up to orthogonal transformation, a solid closed convex cone K in the Euclidean space $\mathbb{R}^{n+1}$ is the epigraph of a nonnegative sublinear function f from $\mathbb{R}^n$ to $\mathbb{R}$. 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.