  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.
