Calculus of Variations and Geometric Measure Theory

E. Bruè - E. Pasqualetto - D. Semola

Rectifiability of RCD(K,N) spaces via $\delta$-splitting maps

created by semola on 22 Jan 2020
modified on 04 Sep 2021


Published Paper

Inserted: 22 jan 2020
Last Updated: 4 sep 2021

Journal: Annales Fennici Mathematici
Volume: 46
Number: 1
Pages: 465-482
Year: 2021
Links: Link to the published version


In this note we give new proofs of rectifiability of RCD(K,N) spaces as metric measure spaces and lower semicontinuity of the essential dimension, via $\delta$-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: Rectifiability, RCD space, Tangent cone