A sharp isoperimetric bound for convex bodies |
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Authors: | Ravi Montenegro |
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Affiliation: | (1) School of Mathematics, Georgia Institute of Technology, 30332-0160 Atlanta, GA, USA |
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Abstract: | We consider the problem of lower bounding the Minkowski content 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. Supported in part by VIGRE grants at Yale University and the Georgia Institute of Technology. |
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