The Geometric Traveling Salesman Problem in the Heisenberg Group
Ferrari, Fausto ; Franchi , Bruno ; Pajot, Hervé
Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, p. 437-480 / Harvested from Project Euclid
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In the Heisenberg group ${\mathbb H}$ (endowed with its Carnot-Carathéodory structure), we prove that a compact set $E \subset {\mathbb H}$ which satisfies an analog of Peter Jones' geometric lemma is contained in a rectifiable curve. This quantitative condition is given in terms of Heisenberg $\beta$ numbers which measure how well the set $E$ is approximated by Heisenberg straight lines.
Publié le : 2007-04-14
Classification:  Heisenberg group,  Carnot-Carathéodory metric,  rectifiable curve,  Traveling Salesman Problem,  28A75 
@article{1190831218,
     author = {Ferrari, Fausto and Franchi , Bruno and Pajot, Herv\'e},
     title = {The Geometric Traveling Salesman Problem in the Heisenberg Group},
     journal = {Rev. Mat. Iberoamericana},
     volume = {23},
     number = {1},
     year = {2007},
     pages = { 437-480},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1190831218}
}

Ferrari, Fausto; Franchi , Bruno; Pajot, Hervé. The Geometric Traveling Salesman Problem in the Heisenberg Group. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp.  437-480. http://gdmltest.u-ga.fr/item/1190831218/