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
相关论文
共 50 条
  • [31] Sub-Riemannian structures in other problems of analysis
    Lanconelli, E
    BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2005, 8B (02): : 273 - 298
  • [32] A Classification of Sub-Riemannian Structures on the Heisenberg Groups
    Biggs, Rory
    Nagy, Peter T.
    ACTA POLYTECHNICA HUNGARICA, 2013, 10 (07) : 41 - 52
  • [33] SUB-RIEMANNIAN GEOMETRY
    STRICHARTZ, RS
    JOURNAL OF DIFFERENTIAL GEOMETRY, 1986, 24 (02) : 221 - 263
  • [34] On extensions of sub-Riemannian structures on Lie groups
    Biggs, Rory
    Nagy, Peter T.
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2016, 46 : 25 - 38
  • [35] Quantum Computational Riemannian and Sub-Riemannian Geodesics
    Shizume, Kosuke
    Nakajima, Takao
    Nakayama, Ryo
    Takahashi, Yutaka
    PROGRESS OF THEORETICAL PHYSICS, 2012, 127 (06): : 997 - 1008
  • [36] On a method to disprove generalized Brunn-Minkowski inequalities
    Juillet, Nicolas
    PROBABILISTIC APPROACH TO GEOMETRY, 2010, 57 : 189 - 198
  • [37] From brunn-minkowski to sharp sobolev inequalities
    Bobkov, S. G.
    Ledoux, M.
    ANNALI DI MATEMATICA PURA ED APPLICATA, 2008, 187 (03) : 369 - 384
  • [38] On discrete Brunn-Minkowski and isoperimetric type inequalities
    Iglesias, David
    Lucas, Eduardo
    Yepes Nicolas, Jesus
    DISCRETE MATHEMATICS, 2022, 345 (01)
  • [39] On discrete Lp Brunn-Minkowski type inequalities
    Hernandez Cifre, Maria A.
    Lucas, Eduardo
    Yepes Nicolas, Jesus
    REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2022, 116 (04)
  • [40] The Openness Conjecture and Complex Brunn-Minkowski Inequalities
    Berndtsson, Bo
    COMPLEX GEOMETRY AND DYNAMICS, 2015, : 29 - 44
12345