Revista Matemática Iberoamericana
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Published online: 2010-12-31
A counterexample for the geometric traveling salesman problem in the Heisenberg groupNicolas Juillet (1) Université de Grenoble I, Saint-Martin-d'Hères, France
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.
Keywords: Heisenberg group, Carnot-Carathéodory metric, rectifiable curve, Traveling Salesman Problem
Juillet Nicolas: A counterexample for the geometric traveling salesman problem in the Heisenberg group. Rev. Mat. Iberoamericana 26 (2010), 1035-1056. doi: 10.4171/RMI/626