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Extremal Properties of Central Half-Spaces for Product Measures

โœ Scribed by F. Barthe


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
216 KB
Volume
182
Category
Article
ISSN
0022-1236

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โœฆ Synopsis


We deal with the isoperimetric and the shift problem for subsets of measure 1ร‚2 in product probability spaces. We prove that the canonical central half-spaces are extremal in particular cases: products of log-concave measures on the real line satisfying precise conditions and products of uniform measures on spheres, or balls. As a corollary, we improve the known log-Sobolev constants for Euclidean balls. We also give some new results about the related question of estimating the volume of sections of unit balls of l p -sums of Minkowski spaces.


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