A counterexample for the geometric traveling salesman problem in the Heisenberg group
Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, p. 1035-1056 / Harvested from Project Euclid
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We are interested in characterizing the compact sets of the Heisenberg group that are contained in a curve of finite length. Ferrari, Franchi and Pajot recently gave a sufficient condition for those sets, adapting a necessary and sufficient condition due to P. Jones in the Euclidean setting. We prove that this condition is not necessary.
Publié le : 2010-09-15
Classification:  Heisenberg group,  Carnot-Carathéodory metric,  rectifiable curve,  Traveling Salesman Problem,  28A75 
@article{1282913831,
     author = {Juillet
, 
Nicolas},
     title = {A counterexample for the geometric traveling salesman problem in the Heisenberg group},
     journal = {Rev. Mat. Iberoamericana},
     volume = {26},
     number = {1},
     year = {2010},
     pages = { 1035-1056},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1282913831}
}

Juillet
, 
Nicolas. A counterexample for the geometric traveling salesman problem in the Heisenberg group. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp.  1035-1056. http://gdmltest.u-ga.fr/item/1282913831/