Weakly non-collapsed RCD spaces are strongly non-collapsed

被引：12
作者：
Brena, Camillo [1 ]
Gigli, Nicola [2 ]
Honda, Shouhei [3 ]
Zhu, Xingyu [4 ]
机构：
[1] Scuola Normale Super Pisa, Pisa, Italy
[2] Scuola Int Super Studi Avanzati, Trieste, Italy
[3] Tohoku Univ, Sendai, Japan
[4] Georgia Inst Technol, Atlanta, GA USA
来源：
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2023年 / 2023卷 / 794期
关键词：
METRIC-MEASURE-SPACES; CURVATURE-DIMENSION CONDITION; LOCAL DIRICHLET SPACES; RICCI CURVATURE; HEAT KERNEL; BOUNDS; EQUIVALENCE; INEQUALITY; BEHAVIOR; FLOW;
D O I：
10.1515/crelle-2022-0071
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms a conjecture raised by De Philippis and the second named author in full generality. One of the auxiliary results of independent interest that we obtain is about the link between the propertiestr(Hess f ) = Af on U subset of X for every f sufficiently regular,m = can on U subset of X for some c > 0,where U subset of X is open and X is a - possibly collapsed - RCD space of essential dimension n.
引用
收藏
页码：215 / 252
页数：38
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