Geodesic
Ricci curvature bounded below and uniform rectifiability
Matthew Hyde1 ; Michele Villa2 ; Ivan Yuri Violo3
1 University of Jyväskylä, Department of Mathematics and Statistics
2 University of Oulu, Mathematics Research Unit, and Universitat Autònoma de Barcelona, Departament de Matématiques
3 Scuola Normale Superiore, Centro di Ricerca Matematica Ennio De Giorgi
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 751–772.

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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.
DOI : 10.54330/afm.153338
Keywords: Uniform rectifiability, metric spaces, Ricci curvature, Lipschitz functions

Matthew Hyde 1 ; Michele Villa 2 ; Ivan Yuri Violo 3

1 University of Jyväskylä, Department of Mathematics and Statistics
2 University of Oulu, Mathematics Research Unit, and Universitat Autònoma de Barcelona, Departament de Matématiques
3 Scuola Normale Superiore, Centro di Ricerca Matematica Ennio De Giorgi 
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Matthew Hyde; Michele Villa; Ivan Yuri Violo. Ricci curvature bounded below and uniform rectifiability. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 751–772. doi : 10.54330/afm.153338. http://geodesic.mathdoc.fr/articles/10.54330/afm.153338/

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