Line transversals to disjoint balls

Details Line transversals to disjoint balls Line transversals to disjoint balls

2006-12-14

arxiv.org/abs/math/0612418v1

Mathematics

Metric Geometry

21 pages, includes figures

Scientific paper

We prove that the set of directions of lines intersecting three disjoint balls in $R^3$ in a given order is a strictly convex subset of $S^2$. We then generalize this result to $n$ disjoint balls in $R^d$. As a consequence, we can improve upon several old and new results on line transversals to disjoint balls in arbitrary dimension, such as bounds on the number of connected components and Helly-type theorems.

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