A sharp isoperimetric bound for convex bodies
Functional Analysis
2007-05-23 v1 Metric Geometry
Probability
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.
Keywords
Cite
@article{arxiv.math/0411018,
title = {A sharp isoperimetric bound for convex bodies},
author = {Ravi Montenegro},
journal= {arXiv preprint arXiv:math/0411018},
year = {2007}
}