Poincare Inequalities and Moment Maps

Bo'az Klartag

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arXiv · 1104.2791

Poincare Inequalities and Moment Maps

Bo'az Klartag

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Abstract

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.

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Bo'az Klartag. 2011-04-14. Poincare Inequalities and Moment Maps. https://arxiv.org/abs/1104.2791

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