A sharp isoperimetric bound for convex bodies

Details A sharp isoperimetric bound for convex bodies A sharp isoperimetric bound for convex bodies

2004-10-31

arxiv.org/abs/math/0411018v1

Israel Journal of Mathematics, volume 153, pp. 267-284, 2006

Mathematics

Functional Analysis

Scientific paper

We consider the problem of lower bounding a generalized Minkowski measure of
subsets of a convex body with a log-concave probability measure, conditioned on
the set size. A bound is given in terms of diameter and set size, which is
sharp for all set sizes, dimensions, and norms. In the case of uniform density
a stronger theorem is shown which is also sharp.

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