SubRiemanniann structures do not satisify Riemannian Brunn--Minkowski inequalities
Differential Geometry
2020-02-05 v1
Abstract
We prove that no Brunn--Minkowski inequality from the Riemannian theories of curvature-dimension and optimal transportation can by satisfied by a strictly subRiemannian structure. Our proof relies on the same method as for the Heisenberg group together with new investigations by Agrachev, Barillari and Rizzi on ample normal geodesics of subRieman-nian structures and the geodesic dimension attached to them.
Keywords
Cite
@article{arxiv.2002.01170,
title = {SubRiemanniann structures do not satisify Riemannian Brunn--Minkowski inequalities},
author = {Nicolas Juillet},
journal= {arXiv preprint arXiv:2002.01170},
year = {2020}
}