Conformal Geometry and Quasiregular Mappings

1988
ISBN: 978-3-540-19342-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1319, 214 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 365 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Vuorinen, Matti

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe

Inhaltsverzeichnis

Conformal geometry.- Modulus and capacity.- Quasiregular mappings.- Boundary behavior.

Über Autor(innen)