  We prove that the isoperimetric profile of a convex domain $\Omega$ with
compact closure in a Riemannian manifold $(M^{n+1},g)$ satisfies a second order
differential inequality which only depends on the dimension of the manifold and
on a lower bound on the Ricci curvature of $\Omega$. Regularity properties of
the profile and topological consequences on isoperimetric regions arise
naturally from this differential point of view.
  Moreover, by integrating the differential inequality we obtain sharp
comparison theorems: not only can we derive an inequality which should be
compared with L\'evy-Gromov Inequality but we also show that if $\text{Ric}\geq
n\delta$ on $\Omega$, then the profile of $\Omega$ is bounded from above by the
profile of the half-space $\mathbb{H}_{\delta}^{n+1}$ in the simply connected
space form with constant sectional curvature $\delta$. As consequence of
isoperimetric comparisons we obtain geometric estimations for the volume and
the diameter of $\Omega$, and for the first non-zero Neumann eigenvalue for the
Laplace operator on $\Omega$.
