  We discuss the Siciak-Zaharjuta extremal function of a real convex body in
C^n, a solution of the homogeneous complex Monge-Ampere equation on the
exterior of the convex body. We determine several conditions under which a
foliation by holomorphic curves can be found in the complement of the convex
body along which the extremal function is harmonic. We study a variational
problem for holomorphic disks in projective space passing through prescribed
points at infinity. The extremal curves are all complex quadric curves, and the
geometry of such curves allows for the determination of the leaves of the
foliation by simple geometric criteria. As a byproduct we encounter a new
invariant of an exterior domain, the Robin indicatrix, which is in some cases
the dual of the Kobayashi indicatrix for a bounded domain.
