Measure comparison and distance inequalities for convex bodies
Functional Analysis
2019-12-03 v1 Classical Analysis and ODEs
Abstract
We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio distance from an arbitrary convex body to the unit balls of subspaces of .
Keywords
Cite
@article{arxiv.1912.00880,
title = {Measure comparison and distance inequalities for convex bodies},
author = {Alexander Koldobsky and Grigoris Paouris and Artem Zvavitch},
journal= {arXiv preprint arXiv:1912.00880},
year = {2019}
}