Inserted: 22 jan 2020
Last Updated: 3 jun 2020
Journal: Ann. Acad. Sci. Fenn. Math.
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