Geodesic
Rectifiability of RCD(K,N) spaces via δ-splitting maps
Elia Bruè1 ; Enrico Pasqualetto2 ; Daniele Semola1
1 Scuola Normale Superiore
2 University of Jyväskylä, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 465-482 Cet article a éte moissonné depuis la source Journal.fi

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  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 $\delta$-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

Elia Bruè 1 ; Enrico Pasqualetto 2 ; Daniele Semola 1

1 Scuola Normale Superiore
2 University of Jyväskylä, Department of Mathematics and Statistics 
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Elia Bruè; Enrico Pasqualetto; Daniele Semola. Rectifiability of RCD(K,N) spaces via δ-splitting maps. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 465-482. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a26/