Matti Vuorinen – författare

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors'' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.

This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.

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.

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.

This volume is a collection of surveys on function theory ineuclidean n-dimensional spaces centered around the theme ofquasiconformal space mappings. These surveys cover or arerelated to several topics including inequalities forconformal invariants and extremal length, distortiontheorems, L(p)-theory of quasiconformal maps, nonlinearpotential theory, variational calculus, value distributiontheory of quasiregular maps, topological properties ofdiscrete open mappings, the action of quasiconformal maps inspecial classes of domains, and global injectivity theorems.The present volume is the first collection of surveys onQuasiconformal Space Mappings since the origin of the theoryin 1960 and this collection provides in compact form accessto a wide spectrum of recent results due to well-knownspecialists.CONTENTS: G.D. Anderson, M.K. Vamanamurthy, M. Vuorinen:Conformal invariants, quasiconformal maps and specialfunctions.- F.W. Gehring: Topics in quasiconformalmappings.- T.Iwaniec: L(p)-theory of quasiregularmappings.- O. Martio: Partial differential equations andquasiregular mappings.- Yu.G. Reshetnyak: On functionalclasses invariant relative to homothetics.- S. Rickman:Picard''s theorem and defect relation for quasiconformalmappings.- U. Srebro: Topological properties of quasiregularmappings.- J. V{is{l{: Domains and maps.- V.A. Zorich: Theglobal homeomorphism theorem for space quasiconformalmappings, its development and related open problems.