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dc.contributor.author	McMullen, Curtis T.
dc.date.accessioned	2009-12-21T20:07:41Z
dc.date.issued	1989
dc.identifier.citation	McMullen, Curtis T. 1989. Amenability, Poincare series and quasiconformal maps. Inventiones Mathematicae 97(1): 95–127.	en_US
dc.identifier.issn	0020-9910	en_US
dc.identifier.issn	1432-1297	en_US
dc.identifier.uri	http://nrs.harvard.edu/urn-3:HUL.InstRepos:3446032
dc.description.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.	en_US
dc.description.sponsorship	Mathematics	en_US
dc.language.iso	en_US	en_US
dc.publisher	Springer Verlag	en_US
dc.relation.isversionof	doi:10.1007/BF01850656	en_US
dc.relation.hasversion	http://www.math.harvard.edu/~ctm/papers/index.html	en_US
dash.license	LAA
dc.title	Amenability, Poincaré Series and Quasiconformal Maps	en_US
dc.type	Journal Article	en_US
dc.description.version	Version of Record	en_US
dc.relation.journal	Inventiones Mathematicae	en_US
dash.depositing.author	McMullen, Curtis T.
dc.date.available	2009-12-21T20:07:41Z

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  Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University

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