Shortest closed curve to contain a sphere in its convex hull
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 $C$.
math.DG↗