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

共 50 条

[31] OPTIMAL MAPS IN NON BRANCHING SPACES WITH RICCI CURVATURE BOUNDED FROM BELOW
Nicola Gigli
Geometric and Functional Analysis, 2012, 22 : 990 - 999
[32] ALMOST RIGIDITY OF WARPED PRODUCTS AND THE STRUCTURE OF SPACES WITH RICCI CURVATURE BOUNDED BELOW
CHEEGER, J
COLDING, TH
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 320 (03): : 353 - 357
[33] On the volume measure of non-smooth spaces with Ricci curvature bounded below
Kell, Martin
Mondino, Andrea
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2018, 18 (02) : 593 - 610
[34] Gromov-Hausdorff limits of Kahler manifolds with Ricci curvature bounded below
Liu, Gang
Szekelyhidi, Gabor
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2022, 32 (02) : 236 - 279
[35] On Compact Riemannian Manifolds with Convex Boundary and Ricci Curvature Bounded from Below
Xiaodong Wang
The Journal of Geometric Analysis, 2021, 31 : 3988 - 4003
[36] On a sharp volume estimate for gradient Ricci solitons with scalar curvature bounded below
Shi Jin Zhang
Acta Mathematica Sinica, English Series, 2011, 27 : 871 - 882
[37] On Compact Riemannian Manifolds with Convex Boundary and Ricci Curvature Bounded from Below
Wang, Xiaodong
JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (04) : 3988 - 4003
[38] Ricci flow of non-collapsed three manifolds whose Ricci curvature is bounded from below
Simon, Miles
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2012, 662 : 59 - 94
[39] Gromov–Hausdorff limits of Kähler manifolds with Ricci curvature bounded below
Gang Liu
Gábor Székelyhidi
Geometric and Functional Analysis, 2022, 32 : 236 - 279
[40] OPTIMAL MAPS IN NON BRANCHING SPACES WITH RICCI CURVATURE BOUNDED FROM BELOW
Gigli, Nicola
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2012, 22 (04) : 990 - 999

← 1 2 3 4 5 →