April 23, 2024Open Access

Answers to questions of Gr\"unbaum and Loewner

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Abstract

We construct a convex body K in Rⁿ, n 5, with the property that there is exactly one hyperplane H passing through c (K), the centroid of K, such that the centroid of K H coincides with c (K). This provides answers to questions of Gr\"unbaum and Loewner for n 5. The proof is based on the existence of non-intersection bodies in these dimensions.

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Myroshnychenko et al. (Tue,) studied this question.

synapsesocial.com/papers/68e6e09eb6db64358765c4c1 https://doi.org/https://doi.org/10.48550/arxiv.2404.15188

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