English

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

Metric Geometry 2022-06-22 v2 Analysis of PDEs Functional Analysis

Abstract

We extend Prekopa's Theorem and the Brunn-Minkowski Theorem from convexity to FF-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.

Keywords

Cite

@article{arxiv.2206.00576,
  title  = {Interpolation, Prekopa and Brunn-Minkowski for $F$-subharmonicity},
  author = {Julius Ross and David Witt Nyström},
  journal= {arXiv preprint arXiv:2206.00576},
  year   = {2022}
}

Comments

v2 References updated. 32 pages. Comments very welcome

R2 v1 2026-06-24T11:36:08.404Z