A Riemannian interpolation inequality à la Borell, Brascamp and Lieb (Q1608540)
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scientific article; zbMATH DE number 1777215
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Riemannian interpolation inequality à la Borell, Brascamp and Lieb |
scientific article; zbMATH DE number 1777215 |
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A Riemannian interpolation inequality à la Borell, Brascamp and Lieb (English)
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8 August 2002
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The aim of this paper is to extend important functional inequalities from the Euclidean case to an \(n\)-dimensional complete, connected, Riemannian \(C^2\)-manifold. These inequalities are interpolation inequalities. The main result is a Riemannian Borell-Brascamp-Lieb inequality. It has as significant corollaries various Riemannian \(p\)-mean inequalities. For instance, for \(p=0\) one obtains a Riemannian version of the Prékopa-Leindler inequality. The method of proof relies on the study of optimal mass transport.
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interpolation inequalities
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Riemannian manifold
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curvature
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goedesics
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optimal mass transport
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