Inserted: 1 sep 2019
Last Updated: 1 sep 2019
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 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.