A strengthening of the dimensional Brunn-Minkowski conjecture implies the (B)-conjecture
Functional Analysis
2026-03-13 v2 Metric Geometry
Abstract
We prove that if a sufficiently regular even log-concave measure satisfies a certain stronger form of the dimensional Brunn-Minkowski conjecture, then it also satisfies the (B)-conjecture. Furthermore, we show that hereditarily convex measures satisfy the aforementioned strengthened form, therefore providing an alternative proof of a recent result by Cordero-Erausquin and Eskenazis stating that a hereditarily convex measure satisfies both conjectures.
Cite
@article{arxiv.2602.23350,
title = {A strengthening of the dimensional Brunn-Minkowski conjecture implies the (B)-conjecture},
author = {Sotiris Armeniakos and Jacopo Ulivelli},
journal= {arXiv preprint arXiv:2602.23350},
year = {2026}
}
Comments
Comments are welcome! v2: Fixed some typographical errors, added further references and made the exposition clearer