Geometric inequalities on Heisenberg groups

被引：20

作者：

Balogh, Zoltan M. ^{[1
]}

Kristaly, Alexandru ^{[2
,3
]}

Sipos, Kinga ^{[1
]}

机构：

[1] Univ Bern, Math Inst, Sidlerstr 5, CH-3012 Bern, Switzerland

[2] Babes Bolyai Univ, Dept Econ, Str Teodor Mihali 58-60, Cluj Napoca 400591, Romania

[3] Obuda Univ, Inst Appl Math, Becsi Ut 96, H-1034 Budapest, Hungary

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2018年 / 57卷 / 02期

基金：

瑞士国家科学基金会;

关键词：

METRIC-MEASURE-SPACES; BRUNN-MINKOWSKI; ISOPERIMETRIC INEQUALITY; SOBOLEV INEQUALITIES; MASS-TRANSPORTATION; RICCI CURVATURE; SHARP SOBOLEV; MANIFOLDS; BRASCAMP;

D O I：

10.1007/s00526-018-1320-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish geometric inequalities in the sub-Riemannian setting of the Heisenberg group H-n. Our results include a natural sub-Riemannian version of the celebrated curvature-dimension condition of Lott-Villani and Sturm and also a geodesic version of the Borell-Brascamp-Lieb inequality akin to the one obtained by Cordero-Erausquin, McCann and Schmuckenschlager. The latter statement implies sub-Riemannian versions of the geodesic Prekopa-Leindler and Brunn-Minkowski inequalities. The proofs are based on optimal mass transportation and Riemannian approximation of Hn developed by Ambrosio and Rigot. These results refute a general point of view, according to which no geometric inequalities can be derived by optimal mass transportation on singular spaces.

引用

页数：41