The Geometric Traveling Salesman Problem in the Heisenberg Group
The Geometric Traveling Salesman Problem in the Heisenberg Group
复制标题
海森堡群中的几何旅行商问题
DOI：
10.4171/rmi/502
复制
发表时间：
2007
影响因子：
1.2
通讯作者：
H. Pajot
中科院分区：
文献类型：
--
作者：
F. Ferrari;B. Franchi;H. Pajot
在海森堡群H(具有Carnot-Carathéodory结构)中，我们证明了满足类似Peter Jones几何引理的紧集E⊂H包含在一条可直曲线中。这个定量条件是用海森堡β数给出的，它衡量集合E被海森堡直线逼近得有多好。
In the Heisenberg group H (endowed with its Carnot-Carathéodory structure), we prove that a compact set E ⊂ H which satisfies an analog of Peter Jones’ geometric lemma is contained in a rectifiable curve. This quantitative condition is given in terms of Heisenberg β numbers which measure how well the set E is approximated by Heisenberg straight lines.