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Conformal geometry and quasiregular mappings

Author: Matti Vuorinen
Publisher: Berlin ; New York : Springer-Verlag, ©1988.
Series: Lecture notes in mathematics (Springer-Verlag), 1319.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Vuorinen, Matti.
Conformal geometry and quasiregular mappings.
Berlin ; New York : Springer-Verlag, ©1988
(DLC) 88014700
(OCoLC)17918430
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Matti Vuorinen
ISBN: 9783540392071 3540392076
OCLC Number: 286153796
Description: 1 online resource (xix, 209 pages) : illustrations.
Contents: Conformal Geometry --
Modulus and Capacity --
Quasiregular Mappings --
Boundary Behavior --
Some Open Problems --
Bibliography --
Index.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1319.
Responsibility: Matti Vuorinen.

Abstract:

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. Teichmller. 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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