Amenability, Poincaré Series and Quasiconformal Maps
| Title: | Amenability, Poincaré Series and Quasiconformal Maps |
| Author: | McMullen, Curtis T. |
| Citation: | McMullen, Curtis T. 1989. Amenability, Poincare series and quasiconformal maps. Inventiones Mathematicae 97(1): 95–127. |
| Full Text & Related Files: |
McMullen_AmenabilityPoincare.pdf (3.113Mb; PDF) 
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| Abstract: | Any covering \(Y \rightarrow X\) of a hyperbolic Riemann surface\(X\) of finite area determines an inclusion of Teichmüller spaces \(Teich(X) \hookrightarrow Teich(Y)\). We show this map is an isometry for the Teichmüller metric if the covering isamenable, and contracting otherwise. In particular, we establish \(\|\Theta\|<1\) for classical Poincaré series (Kra's "Theta conjecture"). The appendix develops the theory of geometric limits of quadratic differentials, used in this paper and a sequel. |
| Published Version: | doi:10.1007/BF01850656 |
| Other Sources: | http://www.math.harvard.edu/~ctm/papers/index.html |
| Terms of Use: | This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA |
| Citable link to this page: | http://nrs.harvard.edu/urn-3:HUL.InstRepos:3446032 |
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