Fortier Bourque, M. (2019) A divergent horocycle in the horofunction compactification of the Teichmüller metric. arXiv, (Unpublished)
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204423.pdf - Submitted Version 428kB |
Publisher's URL: https://arxiv.org/abs/1911.10365
Abstract
We give an example of a horocycle in the Teichmüller space of the five-times-punctured sphere that does not converge in the Gardiner--Masur compactification, or equivalently in the horofunction compactification of the Teichmüller metric. As an intermediate step, we exhibit a simple closed curve whose extremal length is periodic but not constant along the horocycle. The example lifts to any Teichmüller space of complex dimension greater than one via covering constructions.
| Item Type: | Articles |
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| Status: | Unpublished |
| Refereed: | No |
| Glasgow Author(s) Enlighten ID: | Fortier-Bourque, Dr Maxime |
| Authors: | Fortier Bourque, M. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | arXiv |
| Copyright Holders: | Copyright © 2019 The Author |
| Publisher Policy: | Reproduced with the permission of the Author |
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