Sharpening Geometric Inequalities using Computable Symmetry Measures
arXiv:1310.4368 · doi:10.1112/S0025579314000291
Abstract
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the convex body. Since these coefficients are bounded by the dimension but possibly smaller, our inequalities sharpen the original ones. Since they can often be computed efficiently, the improved bounds may also be used to obtain better bounds in approximation algorithms.
This is a preprint. The proper publication in final form is available at journals.cambridge.org, DOI 10.1112/S0025579314000291