Calculus of Variations and Geometric Measure Theory

E. Bruè - E. Pasqualetto - D. Semola

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

created by bruè on 01 Sep 2019
modified on 25 Dec 2022


Published Paper

Inserted: 1 sep 2019
Last Updated: 25 dec 2022

Journal: Journal of the European Mathematical Society (JEMS)
Year: 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.