Ricci curvature bounded below and uniform rectifiability
Hyde, Matthew; Villa, Michele; Violo, Ivan Yuri (2024-12-09)
09.12.2024
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
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Copyright (c) 2024 Annales Fennici Mathematici. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
https://creativecommons.org/licenses/by-nc/4.0/
Copyright (c) 2024 Annales Fennici Mathematici. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
https://creativecommons.org/licenses/by-nc/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202412197469
https://urn.fi/URN:NBN:fi:oulu-202412197469
Tiivistelmä
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.
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.
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- Avoin saatavuus [38840]
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