Theoretical analysis reveals isomorphic Busemann-Petty extensions for distinct measures in convex bodies, highlighting sharp bounds for slicing inequalities and outer volume distances.
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 Lₚ.
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Koldobsky et al. (2022) studied this question.
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