Conformal Geometry and Quasiregular Mappings

Released on by Matti Vuorinen
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  • Conformal Geometry and Quasiregular Mappings Book Detail

  • Author : Matti Vuorinen
  • Release Date : 2006-11-15
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 228
  • ISBN 13 : 3540392076
  • File Size : 77,77 MB
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Conformal Geometry and Quasiregular Mappings by Matti Vuorinen PDF Summary

Book Description: This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook and of a research monograph: it is the first introduction to the subject available in English, contains nearly a hundred exercises, a survey of the subject as well as an extensive bibliography and, finally, a list of open problems.

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Quasiconformal Space Mappings

Quasiconformal Space Mappings

File Size : 74,74 MB
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This volume is a collection of surveys on function theory in euclidean n-dimensional spaces centered around the theme of quasiconformal space mappings. These su