%0 Journal Article
%T Line transversals to disjoint balls
%A Ciprian Borcea
%A Xavier Goaoc
%A Sylvain Petitjean
%J Mathematics
%D 2006
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0612418v1