This is the second part of a work devoted to the theory of epigraphical cones and their applications. 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 $f: \mathbb{R}^n\to \mathbb{R}$. We explore the link between the geometric properties of $K$ and the analytic properties of $f$.

## Citation

JOURNAL OF CONVEX ANALYSIS, 2011, in press.