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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

CiteScore 2017: 0.65

SCImago Journal Rank (SJR) 2017: 1.063
Source Normalized Impact per Paper (SNIP) 2017: 0.833

Mathematical Citation Quotient (MCQ) 2017: 0.86

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Geodesics in the Heisenberg Group

Piotr Hajłasz
  • Corresponding author
  • Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Scott Zimmerman
  • Corresponding author
  • Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-10-29 | DOI: https://doi.org/10.1515/agms-2015-0020


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.

Keywords: Heisenberg group; geodesics; Fourier series; isoperimetric inequality


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About the article

Received: 2015-03-09

Accepted: 2015-10-12

Published Online: 2015-10-29

Citation Information: Analysis and Geometry in Metric Spaces, Volume 3, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2015-0020.

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© 2015 Piotr Hajłasz and Scott Zimmerman. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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