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  3. Hyperbolic Geometry from a Local Viewpoint
  • Cited by 40
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2010
      March 2007
      ISBN:
      9780511618789
      9780521863605
      9780521682244
      DOI:
      https://doi.org/10.1017/CBO9780511618789
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.532kg, 282 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.402kg, 282 Pages
      • Subjects:
      Mathematics (general), Mathematics, Real and Complex Analysis, Geometry and Topology
      Series:
      London Mathematical Society Student Texts (68)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Real and Complex Analysis, Geometry and Topology
    Series:
    London Mathematical Society Student Texts (68)
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    Book description

    Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view; first the density is defined and then the metric via integration. The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains. New material on hyperbolic and hyperbolic-like metrics is presented. These are generalizations of the Kobayashi and Caratheodory metrics for plane domains. The book concludes with applications to holomorphic dynamics including new results and accessible open problems.

    Reviews

    'Here new and interesting results are collected and presented for a target audience of graduate students and researchers, but the first half of the book is well accessible also for undergraduate students, and indeed everyone who is interested in an introduction to hyperbolic geometry.'

    Source: Internationale Mathematische Nachrichten

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