Measure comparison and distance inequalities for convex bodies
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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 $L_p$.
author list (cited authors)
Koldobsky, A., Paouris, G., & Zvavitch, A.