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

is an epigraphical cone if it can be represented as epigraph of a nonnegative sublinear function f from

\mathbb{R}^n R n

to

\mathbb{R} R

. We explore the link between the geometric properties of K and the analytic properties of f.