Plurisubharmonic geodesics and interpolating sets

摘要

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