The hyperbolic metric and geometric function theory
نویسنده
چکیده
The goal is to present an introduction to the hyperbolic metric and various forms of the Schwarz-Pick Lemma. As a consequence we obtain a number of results in geometric function theory.
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I work in geometric group theory, which is the study of groups via the metric spaces on which they act. I use combinatorial, geometric, and topological tools to study the coarse geometry of infinite discrete groups. Coarse geometry is the natural setting for studying discrete groups, since their metric geometry is only well-defined up to bounded distortion. Gromov [65] revolutionized the field ...
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