Some Remarks on Transportation Inequalities and the Slicing Problem
نویسندگان
چکیده
We show that transportation cost inequalities can be used to derive bounds for isotropic constants of convex bodies. We state a conjecture about transportation costs (and discuss support for it) which would have strong consequences for the slicing problem.
منابع مشابه
Some Remarks on Transportation Cost and Related Inequalities
We discuss transportation cost inequalities for uniform measures on convex bodies, and connections with other geometric and functional inequalities. In particular, we show how transportation inequalities can be applied to the slicing problem, and give a new log-Sobolev-type inequality for bounded domains in Rn.
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