Modified Busemann-Petty problem on sections of convex bodies

2004/10/22 by Alexander Koldobsky, A. Koldobsky, Vladyslav Yaskin +6
Mathematics · #52Axx #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities #math.FA #msc:52Axx

paper · pdf · doi:10.48550/arxiv.math/0410496

17 pages

arxiv created 2004/10/22 · openalex publication_date 2004/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Busemann-Petty problem asks whether origin-symmetric convex bodies in ℝⁿ with smaller central hyperplane sections necessarily have smaller n-dimensional volume. It is known that the answer is affirmative if n≤ 4 and negative if n≥ 5. In this article we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions.

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