# Geodesics in the Heisenberg Group

Piotr Hajłasz; Scott Zimmerman

Analysis and Geometry in Metric Spaces (2015)

- Volume: 3, Issue: 1, page 325-337, electronic only
- ISSN: 2299-3274

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topPiotr Hajłasz, and Scott Zimmerman. "Geodesics in the Heisenberg Group." Analysis and Geometry in Metric Spaces 3.1 (2015): 325-337, electronic only. <http://eudml.org/doc/275961>.

@article{PiotrHajłasz2015,

abstract = {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.},

author = {Piotr Hajłasz, Scott Zimmerman},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {Heisenberg group; geodesics; Fourier series; isoperimetric inequality},

language = {eng},

number = {1},

pages = {325-337, electronic only},

title = {Geodesics in the Heisenberg Group},

url = {http://eudml.org/doc/275961},

volume = {3},

year = {2015},

}

TY - JOUR

AU - Piotr Hajłasz

AU - Scott Zimmerman

TI - Geodesics in the Heisenberg Group

JO - Analysis and Geometry in Metric Spaces

PY - 2015

VL - 3

IS - 1

SP - 325

EP - 337, electronic only

AB - 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.

LA - eng

KW - Heisenberg group; geodesics; Fourier series; isoperimetric inequality

UR - http://eudml.org/doc/275961

ER -

## References

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- [9] A. Hurwitz, Sur quelques applications géométriques des séries de Fourier, Ann. Ecole Norm. Sup. 19 (1902) 357–408. Zbl33.0599.02
- [10] S. G. Krantz, H. R. Parks, A primer of real analytic functions. Second edition. Birkhäuser Advanced Texts: Basler Lehrbücher. Birkhäuser Boston, Inc., Boston, MA, 2002.
- [11] R. Montgomery, A tour of subriemannian geometries, their geodesics and applications. Mathematical Surveys and Monographs, 91. American Mathematical Society, Providence, RI, 2002. Zbl1044.53022
- [12] R. Monti, Distances, boundaries and surface measures in Carnot-Carathéodory spaces, PhD thesis 2001. Available at http: //www.math.unipd.it/~monti/PAPERS/TesiFinale.pdf Zbl1032.49045
- [13] R. Monti, Some properties of Carnot-Carathéodory balls in the Heisenberg group, Rend. MatA˙ cc. Lincei 11 (2000) 155–167. Zbl1197.53064
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