  An approach to complex interpolation of compact subsets of $\Bbb C^n$,
including Brunn-Minkowski type inequalities for the capacities of the
interpolating sets, was developed recently by means of plurisubharmonic
geodesics between relative extremal functions of the given sets. Here we show
that a much better control can be achieved by means of the geodesics between
weighted relative extremal functions. In particular, we establish convexity
properties of the capacities that are stronger than those given by the
Brunn-Minkowski inequalities.
