Line Transversals to Disjoint Balls |
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| Authors: | Ciprian Borcea Xavier Goaoc Sylvain Petitjean |
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| Affiliation: | (1) Rider University, Lawrenceville, NJ 08648, USA;(2) LORIA–INRIA Lorraine, Nancy, France;(3) LORIA–CNRS, Nancy, France |
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| 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  . 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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| Keywords: | Transversal Geometric permutation Convexity |
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