Measure comparison and distance inequalities for convex bodies

Alexander Koldobsky, Grigoris Paouris, Artem Zvavitch

Published 2019-12-02Version 1

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 $L_p$.