Epigraphical Cones II

This is the second part of a work devoted to the theory of epigraphical cones and their applications. For part one see this journal 18 (2011) 1171–1196. A convex cone K in the Euclidean space $\mathbb{R}^{n+1}$ is an epigraphical cone if it can be represented as epigraph of a nonnegative sublinear function f from $\mathbb{R}^n$ to $\mathbb{R}$. We explore the link between the geometric properties of K and the analytic properties of f.