Line Transversals to Disjoint Balls
Identifieur interne : 004C36 ( Main/Exploration ); précédent : 004C35; suivant : 004C37Line Transversals to Disjoint Balls
Auteurs : Ciprian Borcea [États-Unis] ; Xavier Goaoc [France] ; Sylvain Petitjean [France]Source :
- Discrete & Computational Geometry [ 0179-5376 ] ; 2008-03-01.
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Abstract
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 $\mathbb {S}^{2}$ . 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.
Url:
DOI: 10.1007/s00454-007-9016-z
Affiliations:
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