  We introduce a new operation, copolar addition, on unbounded convex subsets
of the positive orthant of real euclidean space and establish convexity of the
covolumes of the corresponding convex combinations. The proof is based on a
technique of geodesics of plurisubharmonic functions. As an application, we
show that there are no relative extremal functions inside a non-constant
geodesic curve between two toric relative extremal functions.
