论文标题
恒定宽度的主体，在给定的环中最小面积
Body of constant width with minimal area in a given annulus
论文作者
论文摘要
在本文中，我们解决了以下形状优化问题：在规定的恒定宽度和inradius的集合中找到最小面积的平面域。在文献中，问题归因于Bonnesen，后者在\ cite {bf}中提出了问题。在目前的工作中，我们为问题提供了完整的答案，为各种宽度和inradius选择提供了最佳集合的明确表征。这些最佳集合是特定的Reuleaux多边形。
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.
