Line transversals to disjoint balls

2006/12/14 by Ciprian Borcea, Borcea, Ciprian, Xavier Goaoc +3
Mathematics · #14H50 #52A35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Metric Geometry (math.MG) #math.AG #math.MG #msc:14H50 #msc:52A35

paper · pdf · doi:10.48550/arxiv.math/0612418

21 pages, includes figures

arxiv created 2006/12/14 · arxiv updated 2009/12/01

Abstract

We prove that the set of directions of lines intersecting three disjoint balls in R³ in a given order is a strictly convex subset of S². 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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