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

Authors

  • Elia Bruè Scuola Normale Superiore
  • Enrico Pasqualetto University of Jyväskylä, Department of Mathematics and Statistics
  • Daniele Semola Scuola Normale Superiore

Keywords:

Rectifiability, RCD space, tangent cone

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 \(\delta\)-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.

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Published

2021-06-21

Issue

Vol. 46 No. 1 (2021)

Section

Articles

License

Copyright (c) 2021 The Finnish Mathematical Society

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

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://afm.journal.fi/article/view/109611