Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetric comparisons via viscosity   Viscosity solutions are suitable notions in the study of nonlinear PDEs
justified by estimates established via the maximum principle or the comparison
principle. Here we prove that the isoperimetric profile functions of Riemannian
manifolds with Ricci lower bound are viscosity super-solutions of some
nonlinear differential equations. From these one can derive the isoperimetric
inequalities of L\'evy-Gromov and B\'erard-Besson-Gallot, as well as some new
comparison results.

5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
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The categories of this paper are: eess