TY - JOUR
T1 - Poincare Inequalities and Moment Maps
AU - Klartag, Bo'az
N1 - Supported in part by the Israel Science Foundation and by a Marie Curie Reintegration Grant from the Commission of the European Communities. Thanks to Semyon Alesker, Franck Barthe, Ha¨ım Brezis, DmitryFaifman, Uri Grupel, Greg Kuperberg, Emanuel Milman, Yaron Ostrover, Leonid Polterovich, Yanir Rubinstein and Mikhail Sodin for interesting related discussions. Thanks also to the anonymous referee for encouraging me to learn about K¨ahler-Einstein metrics.
PY - 2013
Y1 - 2013
N2 - We propose a new method for obtaining Poincare-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.
AB - We propose a new method for obtaining Poincare-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.
M3 - مقالة
SN - 0240-2963
VL - 12
SP - 1
EP - 41
JO - Annales de la Faculté des sciences de Toulouse
JF - Annales de la Faculté des sciences de Toulouse
IS - 1
ER -