Ricci curvature bounded below and uniform rectifiability

被引：0

作者：

Hyde, Matthew ^{[1
]}

Villa, Michele ^{[2
,3
]}

Violo, Ivan yuri ^{[4
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, FI-40014 Jyvaskyla, Finland

[2] Univ Oulu, Math Res Unit, FI-90014 Oulu, Finland

[3] Univ Autonoma Barcelona, Dept Matematiques, Bellaterra 08193, Barcelona, Spain

[4] Ctr Ric Matemat Ennio Giorgi, Scuola Normale Super, Piazza Cavalieri 3, I-56100 Pisa, Italy

来源：

ANNALES FENNICI MATHEMATICI | 2024年 / 49卷 / 02期

基金：

欧洲研究理事会; 芬兰科学院; 欧盟地平线“2020”;

关键词：

Uniform rectifiability; metric spaces; Ricci curvature; Lipschitz functions; METRIC-MEASURE-SPACES; ANALYTIC CAPACITY; ALEXANDROV; RIGIDITY; BEHAVIOR; OPERATOR; LIMITS;

D O I：

10.54330/afm.153338

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that Ahlfors-regular RCD spaces are uniformly rectifiable and satisfy the Bilateral Weak Geometric Lemma with Euclidean tangents-a quantitative flatness condition. The same is shown for Ahlfors regular boundaries of non-collapsed RCD spaces. As an application we deduce a type of quantitative differentiation for Lipschitz functions on these spaces.

引用

页码：751 / 772

页数：22

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