Ricci curvature bounded below and uniform rectifiability

Ricci curvature bounded below and uniform rectifiability

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 quantitativ...

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Veröffentlicht in:Annales Fennici Mathematici 2024-12, Vol.49 (2)
Hauptverfasser: Hyde, Matthew, Villa, Michele, Violo, Ivan Yuri
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2737-0690
2737-114X
DOI:10.54330/afm.153338