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Isoperimetric type problems in Riemannian manifolds

The isoperimetric problem : In the classical isoperimetric problem, one is looking for a minimizer of the area functional subject to some volume constraint. This provides a way to construct constant mean curvature hypersurfaces since, when solutions exist and are regular enough, they are characterized by the fact that they are constant mean curvature hypersurfaces. Few information on the solutions of the isoperimetric problem are available even though some progress has been done when the ambient manifold has some special structure.