Sub-Riemannian structures do not satisfy Riemannian Brunn-Minkowski inequalities

被引：6
|
作者：
Juillet, Nicolas [1 ,2 ]
机构：
[1] Univ Strasbourg, IRMA UMR 7501, 7 Rue Rene Descartes, F-67000 Strasbourg, France
[2] CNRS, 7 Rue Rene Descartes, F-67000 Strasbourg, France
来源：
REVISTA MATEMATICA IBEROAMERICANA | 2021年 / 37卷 / 01期
关键词：
Brunn-Minkowski inequality; normal geodesic; Ricci curvature; sub-Riemannian structure; METRIC-MEASURE-SPACES; CURVATURE;
D O I：
10.4171/RMI/1205
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that no Brunn-Minkowski inequality from the Riemannian theories of curvature-dimension and optimal transportation can be satisfied by a strictly sub-Riemannian structure. Our proof relies on the same method as for the Heisenberg group together with new investigations by Agrachev, Barilari and Rizzi on ample normal geodesics of sub-Riemannian structures and the geodesic dimension attached to them.
引用
收藏
页码：177 / 188
页数：12
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