Quasiconformal Space Mappings

A collection of surveys 1960 - 1990
1992
ISBN: 978-3-540-55418-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1508, 150 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 254 g

Reihe: Lecture Notes in Mathematics

This volume is a collection of surveys on function theory in
euclidean n-dimensional spaces centered around the theme of
quasiconformal space mappings. These surveys cover or are
related to several topics including inequalities for
conformal invariants and extremal length, distortion
theorems, L(p)-theory of quasiconformal maps, nonlinear
potential theory, variational calculus, value distribution
theory of quasiregular maps, topological properties of
discrete open mappings, the action of quasiconformal maps in
special classes of domains, and global injectivity theorems.
The present volume is the first collection of surveys on
Quasiconformal Space Mappings since the origin of the theory
in 1960 and this collection provides in compact form access
to a wide spectrum of recent results due to well-known
specialists.
CONTENTS: G.D. Anderson, M.K. Vamanamurthy, M. Vuorinen:

Conformal invariants, quasiconformal maps and special
functions.- F.W. Gehring: Topics in quasiconformal
mappings.- T.Iwaniec: L(p)-theory of quasiregular
mappings.- O. Martio: Partial differential equations and
quasiregular mappings.- Yu.G. Reshetnyak: On functional
classes invariant relative to homothetics.- S. Rickman:

Picard's theorem and defect relation for quasiconformal
mappings.- U. Srebro: Topological properties of quasiregular
mappings.- J. V{is{l{: Domains and maps.- V.A. Zorich: The
global homeomorphism theorem for space quasiconformal
mappings, its development and related open problems.

Zielgruppe

Research

Autoren/Hrsg.

Vuorinen, Matti

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik

Inhaltsverzeichnis

Conformal invariants, quasiconformal maps, and special functions.- Topics in quasiconformal mappings.- L p -theory of quasiregular mappings.- Partial differential equations and quasiregular mappings.- On functional classes invariant relative to homotheties.- Picard’s theorem and defect relation for quasiregular mappings.- Topological properties of quasiregular mappings.- Domains and maps.- The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems.