Body of constant width with minimal area in a given annulus
Metric Geometry
2021-02-09 v2 Optimization and Control
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.
Cite
@article{arxiv.2004.10865,
title = {Body of constant width with minimal area in a given annulus},
author = {Antoine Henrot and Ilaria Lucardesi},
journal= {arXiv preprint arXiv:2004.10865},
year = {2021}
}
Comments
to appear in Journal Ecole Polytechnique