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arXiv · 2004.10865

Body of constant width with minimal area in a given annulus

Antoine Henrot·Ilaria Lucardesi
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Abstract

In this paper we address the following shape optimization problem: find the planar domain of least area, among the sets with prescribed constant width and inradius. In the literature, the problem is ascribed to Bonnesen, who proposed it in \cite{BF}. In the present work, we give a complete answer to the problem, providing an explicit characterization of optimal sets for every choice of width and inradius. These optimal sets are particular Reuleaux polygons.

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Antoine Henrot, Ilaria Lucardesi. 2020-04-22. Body of constant width with minimal area in a given annulus. https://arxiv.org/abs/2004.10865

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