定度极小化长度的周期网络
Periodic networks of fixed degree minimizing length
摘要：
本文研究了$\R^n$中的网络，这些网络在秩为~ $n$的格下是周期性的，并且具有指定度的顶点$d\ge 3$。我们最小化的商网络的长度，受约束的基本区有$n$维体积~ $1$。对于$n=3$和度$3\leq d\leq 6$，我们确定商中顶点数最少的最小化网络，而对于$d\ge 7$，我们给出长度估计。对于一般的$n$，我们用$d=n+1$和$d=2n$确定唯一极小元.
英文摘要：
We study networks in $\R^n$ which are periodic under a lattice of rank~$n$ and have vertices of prescribed degree $d\ge 3$. We minimize the length of the quotient networks, subject to the constraint that the fundamental domain has $n$-dimensional volume~$1$. For $n=3$ and degree $3\leq d\leq 6$ we determine the minimizing networks with the least number of vertices in the quotient, while for $d\ge 7$ we state a length estimate. For general $n$, we determine the unique minimizers with $d=n+1$ and $d=2n$.
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。
