Corpus ID: 237941056

Constancy of the dimension in codimension one and locality of the unit normal on $\mathrm{RCD}(K,N)$ spaces

  title={Constancy of the dimension in codimension one and locality of the unit normal on \$\mathrm\{RCD\}(K,N)\$ spaces},
  author={Elia Bru{\'e} and Enrico Pasqualetto and Daniele Semola},
The aim of this paper is threefold. We first prove that, on RCD(K, N) spaces, the boundary measure of any set with finite perimeter is concentrated on the n-regular set Rn, where n ≤ N is the essential dimension of the space. After, we discuss localization properties of the unit normal providing representation formulae for the perimeter measure of intersections and unions of sets with finite perimeter. Finally, we study Gauss-Green formulae for essentially bounded divergence measure vector… Expand
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