A Helly-type transversal theorem for n-dimensional unit balls

摘要

Let $ mathcal{F} $ be a family of unit balls in $ mathbb{R}^n $ with the property that the mutual distances of the centers are at least $ 2sqrt {2 + sqrt 2 } sim 3.6955 ldots $ . If any n 2 members of $ mathcal{F} $ have a common line transversal, then $ mathcal{F} $ has a line transversal too.