Diophantine approximation on hyperbolic Riemann surfaces
نویسندگان
چکیده
منابع مشابه
Diophantine Approximation on Veech Surfaces
We show that Y. Cheung’s general Z-continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates. The sad...
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This thesis consists of three contributions to the theory of complex approximation on Riemann surfaces. It is known that if E is a closed subset of an open Riemann surface R and f is a holomorphic function on a neighbourhood of E, then it is “usually” not possible to approximate f uniformly by functions holomorphic on all of R. In Chapter 2, we show, however, that for every open Riemann surface...
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— We show that Y. Cheung’s general Z-continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates in an ...
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Let Mg,n be the moduli space of Riemann surfaces of genus g with n punctures. From a complex perspective, moduli space is hyperbolic. For example, Mg,n is abundantly populated by immersed holomorphic disks of constant curvature −1 in the Teichmüller (=Kobayashi) metric. When r = dimC Mg,n is greater than one, however, Mg,n carries no complete metric of bounded negative curvature. Instead, Dehn ...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1986
ISSN: 0001-5962
DOI: 10.1007/bf02399200