Isoperimetry and symmetrization for Sobolev spaces on metric spaces |
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Authors: | Joaquim Martín Mario Milman |
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Affiliation: | 1. Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain;2. Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431, USA |
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Abstract: | 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, Poincaré inequalities, as well as metric versions of the Pólya–Szegö and Faber–Krahn principles. To cite this article: J. Martín, M. Milman, C. R. Acad. Sci. Paris, Ser. I 347 (2009). |
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