Poincaré Inequalities and Moment Maps

Bo’az Klartag[1]

  • [1] School of Mathematical Sciences, Tel-Aviv University, Tel Aviv 69978, Israel

Annales de la faculté des sciences de Toulouse Mathématiques (2013)

  • Volume: 22, Issue: 1, page 1-41
  • ISSN: 0240-2963

Abstract

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We discuss a method for obtaining Poincaré-type inequalities on arbitrary convex bodies in ℝ n . Our technique involves a dual version of Bochner’s formula and a certain moment map, and it also applies to some non-convex sets. In particular, we generalize the central limit theorem for convex bodies to a class of non-convex domains, including the unit balls of ℓ p -spaces in ℝ n for 0 < p < 1 .

How to cite

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Klartag, Bo’az. "Poincaré Inequalities and Moment Maps." Annales de la faculté des sciences de Toulouse Mathématiques 22.1 (2013): 1-41. <http://eudml.org/doc/275324>.

@article{Klartag2013,
abstract = {We discuss a method for obtaining Poincaré-type inequalities on arbitrary convex bodies in $\mathbb\{R\}^n$. Our technique involves a dual version of Bochner’s formula and a certain moment map, and it also applies to some non-convex sets. In particular, we generalize the central limit theorem for convex bodies to a class of non-convex domains, including the unit balls of $\ell _p$-spaces in $\mathbb\{R\}^n$ for $0 &lt; p &lt; 1$.},
affiliation = {School of Mathematical Sciences, Tel-Aviv University, Tel Aviv 69978, Israel},
author = {Klartag, Bo’az},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Poincaré inequalities; dual Bochner formula; moment map; log-concave functions; convex bodies; norm; regularity at infinity},
language = {eng},
month = {6},
number = {1},
pages = {1-41},
publisher = {Université Paul Sabatier, Toulouse},
title = {Poincaré Inequalities and Moment Maps},
url = {http://eudml.org/doc/275324},
volume = {22},
year = {2013},
}

TY - JOUR
AU - Klartag, Bo’az
TI - Poincaré Inequalities and Moment Maps
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2013/6//
PB - Université Paul Sabatier, Toulouse
VL - 22
IS - 1
SP - 1
EP - 41
AB - We discuss a method for obtaining Poincaré-type inequalities on arbitrary convex bodies in $\mathbb{R}^n$. Our technique involves a dual version of Bochner’s formula and a certain moment map, and it also applies to some non-convex sets. In particular, we generalize the central limit theorem for convex bodies to a class of non-convex domains, including the unit balls of $\ell _p$-spaces in $\mathbb{R}^n$ for $0 &lt; p &lt; 1$.
LA - eng
KW - Poincaré inequalities; dual Bochner formula; moment map; log-concave functions; convex bodies; norm; regularity at infinity
UR - http://eudml.org/doc/275324
ER -

References

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