- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:44
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
23
2007
2
The Geometric Traveling Salesman Problem in the Heisenberg Group
Fausto
Ferrari
Università di Bologna, BOLOGNA, ITALY
Bruno
Franchi
Università di Bologna, BOLOGNA, ITALY
Hervé
Pajot
Université Grenoble I, SAINT MARTIN D'HERES CEDEX, FRANCE
Heisenberg group, Carnot-Carath´eodory metric, rectifiable curve, Traveling Salesman Problem
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.
Measure and integration
General
437
480
10.4171/RMI/502
http://www.ems-ph.org/doi/10.4171/RMI/502