Revista Matemática Iberoamericana

The Geometric Traveling Salesman Problem in the Heisenberg Group

Fausto Ferrari, Bruno Franchi , and Hervé Pajot

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Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 23, Number 2 (2007), 437-480.

Dates
First available in Project Euclid: 26 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1190831218

Mathematical Reviews number (MathSciNet)
MR2371434

Zentralblatt MATH identifier
1142.28004

Subjects
Primary: 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]

Keywords
Heisenberg group Carnot-Carathéodory metric rectifiable curve Traveling Salesman Problem

Citation

Ferrari, Fausto; Franchi , Bruno; Pajot, Hervé. The Geometric Traveling Salesman Problem in the Heisenberg Group. Rev. Mat. Iberoamericana 23 (2007), no. 2, 437--480. https://projecteuclid.org/euclid.rmi/1190831218


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