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Measure comparison and distance inequalities for convex bodies

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arxiv 1912.00880 v1 pith:AJDJGGN7 submitted 2019-12-02 math.FA math.CA

Alexander Koldobsky , Grigoris Paouris , Artem Zvavitch This is my paper · ORCID
classification math.FAmath.CA
keywords distanceconvexinequalitiesprovearbitraryballsbodiesbody
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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 $L_p$.

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  1. Isomorphic Busemann--Petty for arbitrary measures: the sharp order

    math.FA 2026-08 conditional novelty 7.0 of 10

    The optimal constant in the isomorphic Busemann-Petty problem for arbitrary even densities has the sharp order √n: a new lower bound C_n ≥ c√n matches the known upper bound C_n ≤ √n.

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