空间中直线与凸集不存在弱 epsilon 网

Otfried Cheong; Xavier Goaoc; Andreas F. Holmsen

doi:10.1007/s00454-023-00573-2

空间中直线与凸集不存在弱 epsilon 网

组合数学 2024-09-06 v3 度量几何

作者: Otfried Cheong , Xavier Goaoc , Andreas F. Holmsen

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摘要

我们证明在 $\mathbb{R}^d$ 中,对于直线与凸集不存在常数大小的弱 $\varepsilon$ -网。

关键词

弱 epsilon 网直线凸集欧氏空间

引用

@article{arxiv.2202.02719,
  title  = {No weak epsilon nets for lines and convex sets in space},
  author = {Otfried Cheong and Xavier Goaoc and Andreas F. Holmsen},
  journal= {arXiv preprint arXiv:2202.02719},
  year   = {2024}
}

备注

Boris Bukh has informed us that our construction can be extended to 2-flats in $\mathbb{R}^4$. The contents of this manuscript was published as part of the paper: O. Cheong, X. Goaoc, A. F. Holmsen, Some New Results on Geometric Transversals. Discrete Comput Geom (2023)

空间中直线与凸集不存在弱 epsilon 网

摘要

关键词

引用

备注

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