Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The isoperimetric profile of a compact Riemannian Manifold for small
  volumes   We show that, the solutions of the isoperimetric problem for small volumes
are $C^{2,\alpha}$-close to small spheres. On the way, we define a class of
submanifolds called pseudo balls, defined by an equation weaker than constancy
of mean curvature. We show that in a neighborhood of each point of a compact
riemannian manifold, there is a unique family concentric pseudo balls which
contains all the pseudo balls $C^{2,\alpha}$-close to small spheres. This
allows us to reduce the isoperimetric problem for small volumes to a
variational problem in finite dimension.

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
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
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat