On polynomially integrable convex bodies

2017/02/01 by Alexander Koldobsky, Alexander Merkurjev, Koldobsky, Alexander +3
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1702.00429

openalex publication_date 2017/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An infinitely smooth convex body in \mathbb Rⁿ is called polynomially integrable of degree N if its parallel section functions are polynomials of degree N. We prove that the only smooth convex bodies with this property in odd dimensions are ellipsoids, if N≥ n-1. This is in contrast with the case of even dimensions and the case of odd dimensions with N

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