Line transversals to disjoint balls
Metric Geometry
2007-05-23 v1 Algebraic Geometry
Abstract
We prove that the set of directions of lines intersecting three disjoint balls in in a given order is a strictly convex subset of . We then generalize this result to disjoint balls in . 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.
Cite
@article{arxiv.math/0612418,
title = {Line transversals to disjoint balls},
author = {Ciprian Borcea and Xavier Goaoc and Sylvain Petitjean},
journal= {arXiv preprint arXiv:math/0612418},
year = {2007}
}
Comments
21 pages, includes figures