Quasiconformal Space Mappings

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.