Amenability, Poincaré Series and Quasiconformal Maps

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Amenability, Poincaré Series and Quasiconformal Maps

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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.
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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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  • FAS Scholarly Articles [7362]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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