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arXiv · 1909.00381

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

Elia Bruè·Enrico Pasqualetto·Daniele Semola
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Abstract

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 [2] 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.

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Elia Bruè, Enrico Pasqualetto, Daniele Semola. 2019-09-01. Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces. https://arxiv.org/abs/1909.00381

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