Extremal Properties of Central Half-Spaces for Product Measures

✍ Scribed by F. Barthe

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 216 KB
• Volume: 182
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3708

✦ Synopsis

We deal with the isoperimetric and the shift problem for subsets of measure 1Â2 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.