  We apply a notion of geodesics of plurisubharmonic functions to interpolation
of compact subsets of $C^n$. Namely, two non-pluripolar, polynomially closed,
compact subsets of $C^n$ are interpolated as level sets $L_t=\{z: u_t(z)=-1\}$
for the geodesic $u_t$ between their relative extremal functions with respect
to any ambient bounded domain. The sets $L_t$ are described in terms of certain
holomorphic hulls. In the toric case, it is shown that the relative
Monge-Amp\`ere capacities of $L_t$ satisfy a dual Brunn-Minkowski inequality.
