Model spaces for sharp isoperimetric inequalities
The author obtain new sharp isoperimetric inequalities on a Riemannian manifold equipped with a probability measure, whose generalized Ricci curvature is bounded from below and generalized dimension and diameter of the convex support are bounded from above. These inequalities are sharp for sets of any given measure and with respect to all parameters (curvature, dimension and diameter). For each choice of the parameters, the model spaces which are extremal for the isoperimetric problem are considered. In particular, the Gromov-Levy and Bakry-Ledoux isoperimetric inequalities are recovered.
scientific article; zbMATH DE number 6108967
scientific article