Geodesic
Ricci curvature bounded below and uniform rectifiability
Matthew Hyde1 ; Michele Villa2 ; Ivan Yuri Violo3
1University of Jyväskylä, Department of Mathematics and Statistics
2University of Oulu, Mathematics Research Unit, and Universitat Autònoma de Barcelona, Departament de Matématiques
3Scuola 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 
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
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