The Brunn-Minkowski Inequality and a Minkowski Problem for Nonlinear Capacity

In this article we study two classical potential-theoretic problems in convex geometry. The first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity, Cap A, where A -capacity is associated with a nonlinear elliptic PDE whose structure is modeled on the p-Laplace equation and whose solutions in an open set are called A -harmonic.