Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The isoperimetric problem via direct method in noncompact metric measure
  spaces with lower Ricci bounds   We establish a structure theorem for minimizing sequences for the
isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces
$(X,\mathsf{d},\mathcal{H}^N)$. Under the sole (necessary) assumption that the
measure of unit balls is uniformly bounded away from zero, we prove that the
limit of such a sequence is identified by a finite collection of isoperimetric
regions possibly contained in pointed Gromov--Hausdorff limits of the ambient
space $X$ along diverging sequences of points. The number of such regions is
bounded linearly in terms of the measure of the minimizing sequence.
  The result follows from a new generalized compactness theorem, which
identifies the limit of a sequence of sets $E_i\subset X_i$ with uniformly
bounded measure and perimeter, where $(X_i,\mathsf{d}_i,\mathcal{H}^N)$ is an
arbitrary sequence of $\mathsf{RCD}(K,N)$ spaces.
  An abstract criterion for a minimizing sequence to converge without losing
mass at infinity to an isoperimetric set is also discussed. The latter
criterion is new also for smooth Riemannian spaces.

37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int