6533b82dfe1ef96bd12912ec

RESEARCH PRODUCT

Rectifiability of RCD(K,N) spaces via δ-splitting maps

Elia BruéEnrico PasqualettoDaniele Semola

subject

Pure mathematicsTangent coneOrder (ring theory)Differential calculusRCD spaceArticlesMathematical proofmetriset avaruudetMeasure (mathematics)matemaattinen analyysidifferentiaaligeometriaConvergence (routing)Metric (mathematics)Mathematics::Metric GeometryRectifiabilityEssential dimensionMathematicstangent cone

description

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. peerReviewed

yearjournalcountryeditionlanguage
2021-06-01
10.5186/aasfm.2021.4627https://doi.org/10.5186/aasfm.2021.4627