We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from the center of the group.
@article{bwmeta1.element.doi-10_1515_agms-2015-0020,
author = {Piotr Haj\l asz and Scott Zimmerman},
title = {Geodesics in the Heisenberg Group},
journal = {Analysis and Geometry in Metric Spaces},
volume = {3},
year = {2015},
zbl = {1328.53039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0020}
}
Piotr Hajłasz; Scott Zimmerman. Geodesics in the Heisenberg Group. Analysis and Geometry in Metric Spaces, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0020/
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