Abstract

A dimension free lower bound is found for isoperimetric constants of product probability measures. From this, some analytic inequalities are derived. 1 Introduction Let (X; d) be a metric space equipped with a non--atomic, separable Borel probability measure ¯. In the present paper we study the quantity Is(¯) = inf ¯ + (A) min(¯(A); 1 \Gamma ¯(A)) (1:1) Key words: Isoperimetry, Poincar'e Inequalities, Cheeger's inequality, Khinchine-- Kahane inequality, Holder's Inequality y Research supported in part by the ISF grant NZX000 and NZX300. This author enjoyed the hospitality of the Faculty of Wiskunde and Informatica, Free University of Amsterdam, while part of this research was carried out. z Research supported in part by an NSF Postdoctoral Fellowship. This author enjoyed the hospitality of Le Cermics, ENPC, France, of the Steklov Mathematical Institute (Sankt Petersburg branch) and of the Department of Mathematics, University of Syktyvkar, Russia, while part of this research...

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