Interpolation, Prekopa and Brunn-Minkowski for F-subharmonicity

Journal article, 2024

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.