论文标题
最短的闭合曲线，在其凸面中包含一个球体
Shortest closed curve to contain a sphere in its convex hull
论文作者
论文摘要
我们表明，在Euclidean 3空间中，任何封闭曲线$γ$都包含其凸面内的单位球体的长度$ l \geq4π$，并且表征了平等的情况。该结果概括了作者最近对Zalgaller的猜想的解决方案。此外，对于$ n $尺寸中的类似问题，我们包括nazarov的估计$ l \ geq cn \ sqrt {n} $，该估计是敏锐的，直至常数$ c $。
We show that in Euclidean 3-space any closed curve $γ$ which contains the unit sphere within its convex hull has length $L\geq4π$, and characterize the case of equality. This result generalizes the authors' recent solution to a conjecture of Zalgaller. Furthermore, for the analogous problem in $n$ dimensions, we include the estimate $L\geq Cn\sqrt{n}$ by Nazarov, which is sharp up to the constant $C$.
