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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 29, 2015

Geodesics in the Heisenberg Group

Piotr Hajłasz and Scott Zimmerman

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.

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Received: 2015-3-9
Accepted: 2015-10-12
Published Online: 2015-10-29

© 2015 Piotr Hajłasz and Scott Zimmerman

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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