A note on the Busemann-Petty problem for bodies of certain invariance

2008/11/10 by Marisa Zymonopoulou, Zymonopoulou, Marisa
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.0811.1593

openalex publication_date 2008/11/10 · 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 hyperplane sections necessarily have smaller volume. The answer is affirmative if n≤ 3 and negative if n≥ 4. We consider a class of convex bodies that have a certain invariance property with respect to their ordered k-tuples of coordinates in \R^kn and prove the corresponding problem.

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