  We describe the harmonic interpolation of convex bodies, and prove a strong
form of the Brunn-Minkowski inequality and characterize its equality case. As
an application we improve a theorem of Berndtsson on the volume of slices of a
pseudoconvex domain. We furthermore apply this to prove subharmonicity of the
expected absolute value of the determinant of a matrix of random vectors
through the connection with zonoids.
