Geodesics in the Heisenberg Group
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.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2015-10-01
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| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/agms-2015-0020 |
| _version_ | 1818733396373798912 |
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| author | Hajłasz Piotr Zimmerman Scott |
| author_facet | Hajłasz Piotr Zimmerman Scott |
| author_sort | Hajłasz Piotr |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T23:48:48Z |
| format | Article |
| id | doaj.art-429bff788afa4eb484947433418283c4 |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-12-17T23:48:48Z |
| publishDate | 2015-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-429bff788afa4eb484947433418283c42022-12-21T21:28:14ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742015-10-013110.1515/agms-2015-0020agms-2015-0020Geodesics in the Heisenberg GroupHajłasz Piotr0Zimmerman Scott1Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USADepartment of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USAWe 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.https://doi.org/10.1515/agms-2015-0020heisenberg group geodesics fourier series isoperimetric inequality |
| spellingShingle | Hajłasz Piotr Zimmerman Scott Geodesics in the Heisenberg Group Analysis and Geometry in Metric Spaces heisenberg group geodesics fourier series isoperimetric inequality |
| title | Geodesics in the Heisenberg Group |
| title_full | Geodesics in the Heisenberg Group |
| title_fullStr | Geodesics in the Heisenberg Group |
| title_full_unstemmed | Geodesics in the Heisenberg Group |
| title_short | Geodesics in the Heisenberg Group |
| title_sort | geodesics in the heisenberg group |
| topic | heisenberg group geodesics fourier series isoperimetric inequality |
| url | https://doi.org/10.1515/agms-2015-0020 |
| work_keys_str_mv | AT hajłaszpiotr geodesicsintheheisenberggroup AT zimmermanscott geodesicsintheheisenberggroup |