A sharp isoperimetric bound for convex bodies

Ravi Montenegro

A sharp isoperimetric bound for convex bodies

泛函分析 2007-05-23 v1 度量几何概率论

作者: Ravi Montenegro

摘要

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.

关键词

convex bodies convex geometry upper bounds

引用

@article{arxiv.math/0411018,
  title  = {A sharp isoperimetric bound for convex bodies},
  author = {Ravi Montenegro},
  journal= {arXiv preprint arXiv:math/0411018},
  year   = {2007}
}

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