Amenability, Poincaré Series and Quasiconformal Maps

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Amenability, Poincaré Series and Quasiconformal Maps

Show simple item record McMullen, Curtis T. 2009-12-21T20:07:41Z 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.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 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 McMullen, Curtis T. 2009-12-21T20:07:41Z

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