Planar radial mean bodies are convex

J. Haddad

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arXiv · 2412.01475

Planar radial mean bodies are convex

J. Haddad

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Abstract

The radial mean bodies of parameter $p>-1$ of a convex body $K \subseteq \mathbb R^n$ are radial sets introduced in [4] by Gardner and Zhang. They are known to be convex for $p\geq 0$. We prove that if $K \subseteq \mathbb R^2$ is a convex body, then its radial mean body of parameter $p$ is convex for every $p \in (-1,0)$.

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BibTeX RIS

J. Haddad. 2024-12-09. Planar radial mean bodies are convex. https://arxiv.org/abs/2412.01475

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