Rectifiability of the reduced boundary for sets of finite perimeter over $\RCD(K,N)$ spaces.

By Elia Brué, Enrico Pasqualetto, Semola Daniele. 2019

64 citations recorded by the source corpus.

This note is devoted to the study of sets of finite perimeter over $\RCD(K,N)$ metric measure spaces. Its aim is to complete the picture about the generalization of De Giorgi's theorem within this framework. Starting from the results of \cite{ABS18} 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.

Subfields: Applied Mathematics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/6faaf265b1fd88b75514d3ee6e60578d7dcd678c