Amenability, Poincar E Series and Quasiconformal Maps
نویسنده
چکیده
Any covering Y ! X of a hyperbolic Riemann surface X of-nite area determines an inclusion of Teichm uller spaces Teich(X) ,! Teich(Y). We show this map is an isometry for the Teichm uller metric if the covering is amenable, and contracting otherwise. In particular , we establish jjjj < 1 for classical Poincar e series (Kra's `Theta conjecture'). The appendix develops the theory of geometric limits of quadratic diierentials, used in this paper and a sequel.
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تاریخ انتشار 1996