A1 Journal article (refereed)
Rectifiability of RCD(K,N) spaces via δ-splitting maps (2021)

Bruè, E., Pasqualetto, E., & Semola, D. (2021). Rectifiability of RCD(K,N) spaces via δ-splitting maps. Annales Fennici Mathematici, 46(1), 465-482. https://doi.org/10.5186/aasfm.2021.4627

JYU authors or editors

Publication details

All authors or editors: Bruè, Elia; Pasqualetto, Enrico; Semola, Daniele

Journal or series: Annales Fennici Mathematici

ISSN: 2737-0690

eISSN: 2737-114X

Publication year: 2021

Volume: 46

Issue number: 1

Pages range: 465-482

Publisher: Finnish Mathematical Society

Publication country: Finland

Publication language: English

DOI: https://doi.org/10.5186/aasfm.2021.4627

Publication open access: Openly available

Publication channel open access: Open Access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/76994

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2001.07911

Abstract

In this note we give simplified proofs of rectifiability of RCD(K,N) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via -splitting maps. The arguments are inspired by the Cheeger-Colding theory for Ricci limits and rely on the second order differential calculus developed by Gigli and on the convergence and stability results by Ambrosio-Honda.

Keywords: mathematical analysis; differential geometry; metric spaces

Free keywords: Rectifiability; RCD space; tangent cone

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 2