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Introduction to the theory of higher-dimensional quasiconformal mappings / Frederick W. Gehring, Gaven J. Martin and Bruce P. Palka.

By: Contributor(s): Material type: TextTextSeries: Mathematical surveys and monographs ; v 216.Publication details: Providence : American Mathematical Society, ©2017.Description: ix, 430 pages : illustrations ; 27 cmISBN:
  • 9780821843604 (alk. paper)
Subject(s): DDC classification:
  • 510MS 23 Am512
Contents:
1. Introduction -- 2. Topology and analysis -- 3. Conformal mappings in Euclidean space -- 4. The moduli of curve families -- 5. Rings and condensers -- 6. Quasiconformal mappings -- 7. Mapping problems -- 8. The Tukia-Väisälä extension theorem -- 9. The Mostow rigidity theorem and discrete Möbius groups.
Summary: Offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory.
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Includes bibliographical references and index.

1. Introduction --
2. Topology and analysis --
3. Conformal mappings in Euclidean space --
4. The moduli of curve families --
5. Rings and condensers --
6. Quasiconformal mappings --
7. Mapping problems --
8. The Tukia-Väisälä extension theorem --
9. The Mostow rigidity theorem and discrete Möbius groups.

Offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory.

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