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A sharp isoperimetric bound for convex bodies

Ravi Montenegro
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Abstract

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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Ravi Montenegro. 2004-10-31. A sharp isoperimetric bound for convex bodies. https://arxiv.org/abs/math/0411018

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