Measure comparison and distance inequalities for convex bodies

2019/12/02 by Alexander Koldobsky, Koldobsky, Alexander, Grigoris Paouris +3 · 2 citations
Mathematics · #52A20 #52B10 #53A15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1912.00880

openalex publication_date 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Cited by

• Extensions of the Busemann-Petty Problem for Arbitrary Measures
• Isomorphic Busemann--Petty for arbitrary measures: the sharp order

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