Line transversals to disjoint balls

Ciprian Borcea; Xavier Goaoc; Sylvain Petitjean

Line transversals to disjoint balls

度量几何 2007-05-23 v1 代数几何

作者: Ciprian Borcea , Xavier Goaoc , Sylvain Petitjean

摘要

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.

关键词

incidence geometry of points and lines convex geometry triangulations

引用

@article{arxiv.math/0612418,
  title  = {Line transversals to disjoint balls},
  author = {Ciprian Borcea and Xavier Goaoc and Sylvain Petitjean},
  journal= {arXiv preprint arXiv:math/0612418},
  year   = {2007}
}

备注

21 pages, includes figures

Line transversals to disjoint balls

摘要

关键词

引用

备注

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