Interpolation, Prekopa and Brunn-Minkowski for $F$-subharmonicity

Abstract

We extend Prekopa's Theorem and the Brunn-Minkowski Theorem from convexity to $F$-subharmonicity. We apply this to the interpolation problem of convex functions and convex sets introducing a new notion of "harmonic interpolation" that we view as a generalization of Minkowski-addition.

v2 References updated. 32 pages. Comments very welcome