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Theory (2008) |
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Abstract |
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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. Categories and Subject Descriptors |
Publication details |
| Download |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=?doi=10.1.1.105.1480 |
| Source |
http://www.loria.fr/~petitjea/papers/socg07.pdf |
| Contributors |
CiteSeerX
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| Repository |
CiteSeerX - Scientific Literature Digital Library and Search Engine (United States) |
| Keywords |
convexity,
lines,
disjoint balls,
Helly-type theorem,
Hadwiger-type theorem,
Hessian
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| Type |
text
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| Language |
English
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| Relation |
10.1.1.15.8526,
10.1.1.94.179,
10.1.1.6.7150,
10.1.1.8.9283,
10.1.1.10.6626,
10.1.1.116.4332,
10.1.1.29.2835,
10.1.1.6.8306
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