Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below

被引：34

作者：

Gigli, Nicola ^{[1
]}

Mondino, Andrea ^{[2
]}

Rajala, Tapio ^{[3
]}

机构：

[1] Univ Nice, Math, F-06108 Nice, France

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

[3] Univ Jyvaskyla, Dept Math & Stat, FI-40014 Jyvaskyla, Finland

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2015年 / 705卷

基金：

芬兰科学院;

关键词：

GEOMETRY; INEQUALITIES; MANIFOLDS; CONES;

D O I：

10.1515/crelle-2013-0052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that in any infinitesimally Hilbertian CD*(K, N)-space at almost every point there exists a Euclidean weak tangent, i.e., there exists a sequence of dilations of the space that converges to a Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof follows by considering iterated tangents and the splitting theorem for infinitesimally Hilbertian CD*(0, N)-spaces.

引用

页码：233 / 244

页数：12

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