0000000000142742
AUTHOR
Daniele Semola
Rectifiability of the reduced boundary for sets of finite perimeter over RCD(K,N) spaces
This paper is devoted to the study of sets of finite perimeter in RCD(K,N) metric measure spaces. Its aim is to complete the picture of the generalization of De Giorgi’s theorem within this framework. Starting from the results of Ambrosio et al. (2019) we obtain uniqueness of tangents and rectifiability for the reduced boundary of sets of finite perimeter. As an intermediate tool, of independent interest, we develop a Gauss–Green integration-by-parts formula tailored to this setting. These results are new and non-trivial even in the setting of Ricci limits. peerReviewed
Rectifiability of RCD(K,N) spaces via δ-splitting maps
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