Ricci curvature bounded below and uniform rectifiability

Authors

  • Matthew Hyde University of Jyväskylä, Department of Mathematics and Statistics
  • Michele Villa University of Oulu, Mathematics Research Unit, and Universitat Autònoma de Barcelona, Departament de Matématiques
  • Ivan Yuri Violo Scuola Normale Superiore, Centro di Ricerca Matematica Ennio De Giorgi
DOI: https://doi.org/10.54330/afm.153338

Keywords:

Uniform rectifiability, metric spaces, Ricci curvature, Lipschitz functions

Abstract

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.
Issue
Vol. 49 No. 2 (2024)
Section
Articles

Published

2024-12-09

How to Cite

Hyde, M., Villa, M., & Violo, I. Y. (2024). Ricci curvature bounded below and uniform rectifiability. Annales Fennici Mathematici, 49(2), 751–772. https://doi.org/10.54330/afm.153338

Copyright (c) 2024 Annales Fennici Mathematici

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