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 -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.
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