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Quasiconformal Space Mappings

Author: Matti Vuorinen

Publisher: Springer

Published: 2006-11-14

Total Pages: 156

ISBN-13: 3540470611

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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.

Book Synopsis Quasiconformal Space Mappings by : Matti Vuorinen

Download or read book Quasiconformal Space Mappings written by Matti Vuorinen and published by Springer. This book was released on 2006-11-14 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quasiconformal Space Mappings

Author: Matti Vuorinen

Publisher:

Published: 2014-01-15

Total Pages: 160

ISBN-13: 9783662164204

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Book Synopsis Quasiconformal Space Mappings by : Matti Vuorinen

Download or read book Quasiconformal Space Mappings written by Matti Vuorinen and published by . This book was released on 2014-01-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Moduli of Families of Curves for Conformal and Quasiconformal Mappings

Author: Alexander Vasil'ev

Publisher: Springer

Published: 2004-10-19

Total Pages: 222

ISBN-13: 3540454373

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The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmüller spaces. The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Many of them are grouped around two-point distortion theorems. Montel's functions and functions with fixed angular derivatives are also considered. The last portion of problems is directed to the extension of the modulus varying the complex structure of the underlying Riemann surface that sheds some new light on the metric problems of Teichmüller spaces.

Book Synopsis Moduli of Families of Curves for Conformal and Quasiconformal Mappings by : Alexander Vasil'ev

Download or read book Moduli of Families of Curves for Conformal and Quasiconformal Mappings written by Alexander Vasil'ev and published by Springer. This book was released on 2004-10-19 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmüller spaces. The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Many of them are grouped around two-point distortion theorems. Montel's functions and functions with fixed angular derivatives are also considered. The last portion of problems is directed to the extension of the modulus varying the complex structure of the underlying Riemann surface that sheds some new light on the metric problems of Teichmüller spaces.

Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces

Author: Yunping Jiang

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 386

ISBN-13: 0821853406

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This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, held in honor of Clifford J. Earle, from October 2-3, 2010, in Syracuse, New York. This volume includes a wide range of papers on Teichmuller theory and related areas. It provides a broad survey of the present state of research and the applications of quasiconformal mappings, Riemann surfaces, complex dynamical systems, Teichmuller theory, and geometric function theory. The papers in this volume reflect the directions of research in different aspects of these fields and also give the reader an idea of how Teichmuller theory intersects with other areas of mathematics.

Book Synopsis Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces by : Yunping Jiang

Download or read book Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces written by Yunping Jiang and published by American Mathematical Soc.. This book was released on 2012 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, held in honor of Clifford J. Earle, from October 2-3, 2010, in Syracuse, New York. This volume includes a wide range of papers on Teichmuller theory and related areas. It provides a broad survey of the present state of research and the applications of quasiconformal mappings, Riemann surfaces, complex dynamical systems, Teichmuller theory, and geometric function theory. The papers in this volume reflect the directions of research in different aspects of these fields and also give the reader an idea of how Teichmuller theory intersects with other areas of mathematics.

Lectures on Quasiconformal Mappings

Author: Lars Valerian Ahlfors

Publisher: American Mathematical Soc.

Published: 2006-07-14

Total Pages: 178

ISBN-13: 0821836447

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Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.

Book Synopsis Lectures on Quasiconformal Mappings by : Lars Valerian Ahlfors

Download or read book Lectures on Quasiconformal Mappings written by Lars Valerian Ahlfors and published by American Mathematical Soc.. This book was released on 2006-07-14 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.

Quasiconformal Mappings and Analysis

Author: Peter Duren

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 379

ISBN-13: 1461206057

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In honor of Frederick W. Gehring on the occasion of his 70th birthday, an international conference on ""Quasiconformal mappings and analysis"" was held in Ann Arbor in August 1995. The 9 main speakers of the conference (Astala, Earle, Jones, Kra, Lehto, Martin, Pommerenke, Sullivan, and Vaisala) provide broad expository articles on various aspects of quasiconformal mappings and their relations to other areas of analysis. 12 other distinguished mathematicians contribute articles to this volume.

Book Synopsis Quasiconformal Mappings and Analysis by : Peter Duren

Download or read book Quasiconformal Mappings and Analysis written by Peter Duren and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honor of Frederick W. Gehring on the occasion of his 70th birthday, an international conference on ""Quasiconformal mappings and analysis"" was held in Ann Arbor in August 1995. The 9 main speakers of the conference (Astala, Earle, Jones, Kra, Lehto, Martin, Pommerenke, Sullivan, and Vaisala) provide broad expository articles on various aspects of quasiconformal mappings and their relations to other areas of analysis. 12 other distinguished mathematicians contribute articles to this volume.

Quasiconformal Mappings and Their Applications

Author: Saminathan Ponnusamy

Publisher:

Published: 2007

Total Pages: 378

ISBN-13:

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"Quasiconformal Mappings and their Applications covers conformal invariance and conformally invariant metrics, hyperbolic-type metrics and hyperbolic geodesics, isometries of relative metrics, uniform spaces and Gromov hyperbolicity, quasiregular mappings and quasiconformal mappings in n-space, universal Teichmuller space and related topics, quasiminimizers and potential theory, and numerical conformal mapping and circle packings."--BOOK JACKET.

Book Synopsis Quasiconformal Mappings and Their Applications by : Saminathan Ponnusamy

Download or read book Quasiconformal Mappings and Their Applications written by Saminathan Ponnusamy and published by . This book was released on 2007 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Quasiconformal Mappings and their Applications covers conformal invariance and conformally invariant metrics, hyperbolic-type metrics and hyperbolic geodesics, isometries of relative metrics, uniform spaces and Gromov hyperbolicity, quasiregular mappings and quasiconformal mappings in n-space, universal Teichmuller space and related topics, quasiminimizers and potential theory, and numerical conformal mapping and circle packings."--BOOK JACKET.

QUASICONFORMAL MAPPINGS IN SPACE.

Author: MAVINA KRISHNA VAMANAMURTHY

Publisher:

Published: 1969

Total Pages: 94

ISBN-13:

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Book Synopsis QUASICONFORMAL MAPPINGS IN SPACE. by : MAVINA KRISHNA VAMANAMURTHY

Download or read book QUASICONFORMAL MAPPINGS IN SPACE. written by MAVINA KRISHNA VAMANAMURTHY and published by . This book was released on 1969 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quasiconformal Mappings and Sobolev Spaces

Author: V.M. Gol'dshtein

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 389

ISBN-13: 9400919220

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'Ht moi ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ... "'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'~re of this series

Book Synopsis Quasiconformal Mappings and Sobolev Spaces by : V.M. Gol'dshtein

Download or read book Quasiconformal Mappings and Sobolev Spaces written by V.M. Gol'dshtein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Ht moi ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ... "'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'~re of this series

Conformally Invariant Metrics and Quasiconformal Mappings

Author: Parisa Hariri

Publisher: Springer Nature

Published: 2020-04-11

Total Pages: 504

ISBN-13: 3030320685

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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.

Book Synopsis Conformally Invariant Metrics and Quasiconformal Mappings by : Parisa Hariri

Download or read book Conformally Invariant Metrics and Quasiconformal Mappings written by Parisa Hariri and published by Springer Nature. This book was released on 2020-04-11 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.