Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constancy of the dimension in codimension one and locality of the unit
  normal on $\mathrm{RCD}(K,N)$ spaces   The aim of this paper is threefold. We first prove that, on
$\mathrm{RCD}(K,N)$ spaces, the boundary measure of any set with finite
perimeter is concentrated on the $n$-regular set $\mathcal{R}_n$, where $n\le
N$ 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 fields, sharpening the analysis in \cite{BuffaComiMiranda19}.\\
These tools are fundamental for the development of a regularity theory for
local perimeter minimizers on $\mathrm{RCD}(K,N)$ spaces in
\cite{MondinoSemola21}.

15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex