Isoperimetry and Symmetrization for Sobolev spaces on metric spaces
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inequalitiesmetricspacesisoperimetrysobolevsymmetrizationallowapplications
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Using isoperimetry we obtain new symmetrization inequalities that allow us to provide a unified framework to study Sobolev inequalities in metric spaces. The applications include concentration inequalities, as well as metric versions of the P\'{o}% lya-Szeg\"{o} and Faber-Krahn principles.
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