Quasiconformal Space Mappings: A collection of surveys 1960–1990

G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen (auth.), Matti Vuorinen (eds.)9780387554181, 0387554181, 3540554181

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.

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Table of contents :
Conformal invariants, quasiconformal maps, and special functions….Pages 1-19
Topics in quasiconformal mappings….Pages 20-38
L p -theory of quasiregular mappings….Pages 39-64
Partial differential equations and quasiregular mappings….Pages 65-79
On functional classes invariant relative to homotheties….Pages 80-92
Picard’s theorem and defect relation for quasiregular mappings….Pages 93-103
Topological properties of quasiregular mappings….Pages 104-118
Domains and maps….Pages 119-131
The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems….Pages 132-148