Line transversals to disjoint balls

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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.
21 pages, includes figures

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Metric Geometry, Algebraic Geometry, 52A35, 14H50

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http://salesiana.dossiersoluciones.com/handle/123456789/119928

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0612418
 http://arxiv.org/abs/math/0612418

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arXiv