Extremal functions for real convex bodies

Abstract

We study the smoothness of the Siciak-Zaharjuta extremal function associated to a convex body in $\mathbb{R}^2$. We also prove a formula relating the complex equilibrium measure of a convex body in $\mathbb{R}^n$ to that of its Robin indicatrix. The main tool we use are extremal ellipses.

27 pages, 4 figures