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Author: Kirsi Peltonen
Publisher:
ISBN: 9789514106828
Category : Quasiconformal mappings
Languages : en
Pages : 48
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Book Description
Author: Kirsi Peltonen
Publisher:
ISBN: 9789514106828
Category : Quasiconformal mappings
Languages : en
Pages : 48
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Book Description
Author: Shupei Wang
Publisher:
ISBN: 9789514107382
Category : Differential equations
Languages : en
Pages : 72
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Book Description
Author: Seppo Rickman
Publisher: Springer Science & Business Media
ISBN: 3642782019
Category : Mathematics
Languages : en
Pages : 221
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Book Description
Quasiregular Mappings extend quasiconformal theory to the noninjective case.They give a natural and beautiful generalization of the geometric aspects ofthe theory of analytic functions of one complex variable to Euclidean n-space or, more generally, to Riemannian n-manifolds. This book is a self-contained exposition of the subject. A braod spectrum of results of both analytic and geometric character are presented, and the methods vary accordingly. The main tools are the variational integral method and the extremal length method, both of which are thoroughly developed here. Reshetnyak's basic theorem on discreteness and openness is used from the beginning, but the proof by means of variational integrals is postponed until near the end. Thus, the method of extremal length is being used at an early stage and leads, among other things, to geometric proofs of Picard-type theorems and a defect relation, which are some of the high points of the present book.
Author: Jorma Jormakka
Publisher:
ISBN:
Category : Quasiconformal mappings
Languages : en
Pages : 52
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Book Description
Author: Matti Vuorinen
Publisher: Springer
ISBN: 3540470611
Category : Mathematics
Languages : en
Pages : 156
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Book Description
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.
Author: NATHAN RAY SODERBORG
Publisher:
ISBN:
Category :
Languages : en
Pages : 222
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Book Description
quasiregular mapping induced by T:A($\Omega \sp\prime )\to \rm A \subset A(\Omega)$ is bounded above by $\Vert$T$\Vert \sp{\rm n \sp2}$.
Author: Matti Vuorinen
Publisher: Springer
ISBN: 3540392076
Category : Mathematics
Languages : en
Pages : 228
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Book Description
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.
Author:
Publisher: World Scientific
ISBN:
Category :
Languages : en
Pages : 1001
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Book Description
Author: Matti Vuorinen
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 550
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Book Description
Author: Mark Lʹvovich Agranovskiĭ
Publisher: American Mathematical Soc.
ISBN: 0821841505
Category : Mathematics
Languages : en
Pages : 482
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Book Description
The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.
