Convex bodies with pairs of sections associated by reflections

2024/07/03 by Morales-Amaya, Efren
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2407.02755

Abstract

In this work we prove that if for a pair of convex bodies K₁, K₂ ⊂ ℝⁿ, n ≥ 3, there exists a hyperplane H and two distinct points p₁ and p₂ in ℝⁿ ∖ H such that for every (n-2)-plane M ⊂ H, there exists a reflection mapping the hypersection of K₁ defined by aff\p₁, M\ onto the hypersection of K₂ defined by aff\p₂, M\, then there exists a reflection which maps K₁ onto K₂.

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