Fortier Bourque, M. (2016) The converse of the Schwarz Lemma is false. Annales Academiae Scientiarum Fennicae-Mathematica, 41, pp. 235-241. (doi: 10.5186/aasfm.2016.4115)
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Publisher's URL: http://www.acadsci.fi/mathematica/Vol41/FortierBourque.html
Abstract
Let h : X → Y be a homeomorphism between hyperbolic surfaces with finite topology. If h is homotopic to a holomorphic map, then every closed geodesic in X is at least as long as the corresponding geodesic in Y, by the Schwarz Lemma. The converse holds trivially when X and Y are disks or annuli, and it holds when X and Y are closed surfaces by a theorem of Thurston. We prove that the converse is false in all other cases, strengthening a result of Masumoto.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| 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 |
| Journal Name: | Annales Academiae Scientiarum Fennicae-Mathematica |
| Journal Abbr.: | Ann. Acad. Sci. Fenn. Math. |
| Publisher: | Suomalainen Tiedeakatemia |
| ISSN: | 1798-2383 |
| ISSN (Online): | 1239-629X |
| Copyright Holders: | Copyright © 2016 Academia Scientiarum Fennica |
| First Published: | First published in Annales Academiae Scientiarum Fennicae-Mathematica 41: 235-241 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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