关于欧几里得空间中点的构形的连续展开式
On continuous expansions of configurations of points in Euclidean space
摘要：
对于欧几里得空间$E^d$中有序点$p=(p_{1},...,\p_{N})$和$q=(q_{1},...,q_{N})$的任何两种配置，使得$q$是$p$的扩展，存在从$p$到$q$的2d维连续扩展; Bezdek和Connelly利用这一点证明了平面情况下的Kneser-Poulsen猜想。在本文中，我们表明，这种结构是最佳的意义上，对于任何$d \ge 2$存在配置的$(d+1)^2$点$p$和$q$在$E^d$，使$q$是一个扩展的$p$，但没有连续的扩展从$p$到$q$在小于2 d。我们证明中使用的技术是完全基本的。
英文摘要：
For any two configurations of ordered points $p=(p_{1},...,\p_{N})$ and $q=(q_{1},...,q_{N})$ in Euclidean space $E^d$ such that $q$ is an expansion of $p$, there exists a continuous expansion from $p$ to $q$ in dimension 2d; Bezdek and Connelly used this to prove the Kneser-Poulsen conjecture for the planar case. In this paper, we show that this construction is optimal in the sense that for any $d \ge 2$ there exists configurations of $(d+1)^2$ points $p$ and $q$ in $E^d$ such that $q$ is an expansion of $p$ but there is no continuous expansion from $p$ to $q$ in dimension less than 2d. The techniques used in our proof are completely elementary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
