Hardcover ISBN:  9780821819838 
Product Code:  SURV/76 
List Price:  $116.00 
MAA Member Price:  $104.40 
AMS Member Price:  $92.80 
Electronic ISBN:  9781470413033 
Product Code:  SURV/76.E 
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Book DetailsMathematical Surveys and MonographsVolume: 76; 2000; 372 ppMSC: Primary 30; 32;
The Teichmüller space \(T(X)\) is the space of marked conformal structures on a given quasiconformal surface \(X\). This volume uses quasiconformal mapping to give a unified and uptodate treatment of \(T(X)\). Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type.
The book provides a treatment of deformations of complex structures on infinite Riemann surfaces and gives background for further research in many areas. These include applications to fractal geometry, to threedimensional manifolds through its relationship to Kleinian groups, and to onedimensional dynamics through its relationship to quasisymmetric mappings. Many research problems in the application of function theory to geometry and dynamics are suggested.ReadershipGraduate students, research and applied mathematicians and physicists interested in functions of a complex variable, several complex variables and analytic spaces, particularly mathematical foundations of deformation theory.

Table of Contents

Chapters

1. Quasiconformal mapping

2. Riemann surfaces

3. Quadratic differentials, Part I

4. Quadratic differentials, Part II

5. Teichmüller equivalence

6. The Bers embedding

7. Kobayashi’s metric on Teichmüller space

8. Isomorphisms and automorphisms

9. Teichmüller uniqueness

10. The mapping class group

11. JenkinsStrebel differentials

12. Measured foliations

13. Obstacle problems

14. Asymptotic Teichmüller space

15. Asymptotically extremal maps

16. Universal Teichmüller space

17. Substantial boundary points

18. Earthquake mappings


Additional Material

Reviews

The goal of this book is stated in the excellent preface: ‘to provide background for applications of Teichmüller theory to dynamical systems’ … The extensive bibliography is instructive … a very interesting book … The treatment is clear and methodical … probably be possible to read this as an introductory text, yet there is much that is relatively new, innovative, and perhaps, percipient.
Bulletin of the LMS 
[The authors] have produced a formidable treatise on the modern theories of quasiconformal mappings, Riemann surfaces and Teichmüller spaces. They have gathered, into a unified exposition, results which … have not previously been found in book form … Many of the approaches and results are new, others are more detailed than can be found elsewhere … this monograph is now the standard reference on twodimensional quasiconformal mappings and Teichmüller theory and is likely to remain so for many years.
Mathematical Reviews 
Brings to the literature the current state of the analytic theory of Teichmüuller spaces … a thorough report on the latest developments … a solid exposition of most of the classical foundations … [this book] is a real service to the community … an important addition to the literature … topics are discussed very thoroughly; some shed a lot of new light on the material.
Bulletin of the AMS


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The Teichmüller space \(T(X)\) is the space of marked conformal structures on a given quasiconformal surface \(X\). This volume uses quasiconformal mapping to give a unified and uptodate treatment of \(T(X)\). Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type.
The book provides a treatment of deformations of complex structures on infinite Riemann surfaces and gives background for further research in many areas. These include applications to fractal geometry, to threedimensional manifolds through its relationship to Kleinian groups, and to onedimensional dynamics through its relationship to quasisymmetric mappings. Many research problems in the application of function theory to geometry and dynamics are suggested.
Graduate students, research and applied mathematicians and physicists interested in functions of a complex variable, several complex variables and analytic spaces, particularly mathematical foundations of deformation theory.

Chapters

1. Quasiconformal mapping

2. Riemann surfaces

3. Quadratic differentials, Part I

4. Quadratic differentials, Part II

5. Teichmüller equivalence

6. The Bers embedding

7. Kobayashi’s metric on Teichmüller space

8. Isomorphisms and automorphisms

9. Teichmüller uniqueness

10. The mapping class group

11. JenkinsStrebel differentials

12. Measured foliations

13. Obstacle problems

14. Asymptotic Teichmüller space

15. Asymptotically extremal maps

16. Universal Teichmüller space

17. Substantial boundary points

18. Earthquake mappings

The goal of this book is stated in the excellent preface: ‘to provide background for applications of Teichmüller theory to dynamical systems’ … The extensive bibliography is instructive … a very interesting book … The treatment is clear and methodical … probably be possible to read this as an introductory text, yet there is much that is relatively new, innovative, and perhaps, percipient.
Bulletin of the LMS 
[The authors] have produced a formidable treatise on the modern theories of quasiconformal mappings, Riemann surfaces and Teichmüller spaces. They have gathered, into a unified exposition, results which … have not previously been found in book form … Many of the approaches and results are new, others are more detailed than can be found elsewhere … this monograph is now the standard reference on twodimensional quasiconformal mappings and Teichmüller theory and is likely to remain so for many years.
Mathematical Reviews 
Brings to the literature the current state of the analytic theory of Teichmüuller spaces … a thorough report on the latest developments … a solid exposition of most of the classical foundations … [this book] is a real service to the community … an important addition to the literature … topics are discussed very thoroughly; some shed a lot of new light on the material.
Bulletin of the AMS