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Hyperbolic Geometry from a Local Viewpoint

$63.99 (P)

Part of London Mathematical Society Student Texts

  • Date Published: April 2007
  • availability: Available
  • format: Paperback
  • isbn: 9780521682244

$ 63.99 (P)

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About the Authors
  • 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.

    • Entirely self-contained text on hyperbolic geometry for plane domains, accessible to upper-level undergraduate and graduate students yet also suitable for academic researchers
    • Contains over 250 exercises and worked examples
    • Presents brand new material on hyperbolic and hyperbolic-like matrices
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    Reviews & endorsements

    '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.' Internationale Mathematische Nachrichten

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    Product details

    • Date Published: April 2007
    • format: Paperback
    • isbn: 9780521682244
    • length: 282 pages
    • dimensions: 229 x 152 x 16 mm
    • weight: 0.402kg
    • contains: 32 b/w illus. 236 exercises
    • availability: Available
  • Table of Contents

    1. Elementary transformations
    2 Hyperbolic metric in the unit disk
    3. Holomorphic functions
    4. Topology and uniformization
    5. Discontinuous groups
    6 Fuchsian groups
    7. General hyperbolic metric
    8. The Kobayashi metric
    9. The Caratheodory pseudo metric
    10. Contraction properties
    11. Applications
    12 Applications II
    13. Applications III
    14. Estimating hyperbolic densities
    15. Uniformly perfect domains
    16 Appendix: Elliptic functions

  • Authors

    Linda Keen, City University of New York
    Linda Keen is a Professor of Mathematics at the City University of New York, Lehman College and the Graduate Center.

    Nikola Lakic, City University of New York
    Nikola Lakic is an Associate Professor of Mathematics at the City University of New York, Lehman College and the Graduate Center.

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