English

Geodesics in the Heisenberg group

Metric Geometry 2015-10-21 v5

Abstract

We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn\mathbb{H}^n. The proof is based on a new isoperimetric inequality for closed curves in R2n\mathbb{R}^{2n}. We also prove that the Carnot-Carath\'eodory metric is real analytic away from the center of the group.

Keywords

Cite

@article{arxiv.1412.1797,
  title  = {Geodesics in the Heisenberg group},
  author = {Piotr Hajłasz and Scott Zimmerman},
  journal= {arXiv preprint arXiv:1412.1797},
  year   = {2015}
}