Softcover ISBN:  9780821849866 
Product Code:  CBMS/113 
List Price:  $41.00 
Individual Price:  $32.80 
Electronic ISBN:  9781470415716 
Product Code:  CBMS/113.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
AMS Member Price:  $30.40 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 113; 2010; 118 ppMSC: Primary 20; 30; 32; 37; Secondary 11; 14;
This book is the companion to the CBMS lectures of Scott Wolpert at Central Connecticut State University. The lectures span across areas of research progress on deformations of hyperbolic surfaces and the geometry of the WeilPetersson metric. The book provides a generally selfcontained course for graduate students and postgraduates. The exposition also offers an update for researchers; material not otherwise found in a single reference is included.
A unified approach is provided for an array of results. The exposition covers Wolpert's work on twists, geodesiclengths and the WeilPetersson symplectic structure; Wolpert's expansions for the metric, its LeviCivita connection and Riemann tensor. The exposition also covers Brock's twisting limits, visual sphere result and pants graph quasi isometry, as well as the BrockMasurMinsky construction of ending laminations for WeilPetersson geodesics. The rigidity results of MasurWolf and DaskalopoulosWentworth, following the approach of Yamada, are included. The book concludes with a generally selfcontained treatment of the McShaneMirzakhani length identity, Mirzakhani's volume recursion, approach to WittenKontsevich theory by hyperbolic geometry, and prime simple geodesic theorem.
Lectures begin with a summary of the geometry of hyperbolic surfaces and approaches to the deformation theory of hyperbolic surfaces. General expositions are included on the geometry and topology of the moduli space of Riemann surfaces, the \(CAT(0)\) geometry of the augmented Teichmüller space, measured geodesic and ending laminations, the deformation theory of the prescribed curvature equation, and the Hermitian description of Riemann tensor. New material is included on estimating orbit sums as an approach for the potential theory of surfaces.A copublication of the AMS and CBMS.
ReadershipGraduate students and research mathematicians interested in Riemann surfaces, moduli spaces of Riemann surfaces, and Teichmüller theory.

Table of Contents

Chapters

Chapter 1. Preliminaries

Chapter 2. Teichmüller space and horizontal strip deformations

Chapter 3. Geodesiclengths, twists and symplectic geometry

Chapter 4. Geometry of the augmented Teichmüller space, part 1

Chapter 5. Geometry of the augmented Teichmüller space, part 2

Chapter 6. Geometry of the augmented Teichmüller space, part 3

Chapter 7. Deformations of hyperbolic metrics and the curvature tensor

Chapter 8. Collar expansions and exponentialdistance sums

Chapter 9. Train tracks and the Mirzakhani volume recursion

Chapter 10. Mirzakhani prime simple geodesic theorem


Additional Material

Reviews

...this book is that it introduces some topics that are at the frontier of current research, which are not discussed in other books on moduli spaces of Riemann surfaces. This book will be a good reference for researchers working in the field as well as those that just want to take a glimpse of the interconnection between different aspects of Teichmüller theory.
Mathematical Reviews 
[The author] takes pains to present a good deal of guidance as regards the indicated research literature and, indeed, each chapter ends with a useful recommendation of further readings.
Michael Berg, MAA Online


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This book is the companion to the CBMS lectures of Scott Wolpert at Central Connecticut State University. The lectures span across areas of research progress on deformations of hyperbolic surfaces and the geometry of the WeilPetersson metric. The book provides a generally selfcontained course for graduate students and postgraduates. The exposition also offers an update for researchers; material not otherwise found in a single reference is included.
A unified approach is provided for an array of results. The exposition covers Wolpert's work on twists, geodesiclengths and the WeilPetersson symplectic structure; Wolpert's expansions for the metric, its LeviCivita connection and Riemann tensor. The exposition also covers Brock's twisting limits, visual sphere result and pants graph quasi isometry, as well as the BrockMasurMinsky construction of ending laminations for WeilPetersson geodesics. The rigidity results of MasurWolf and DaskalopoulosWentworth, following the approach of Yamada, are included. The book concludes with a generally selfcontained treatment of the McShaneMirzakhani length identity, Mirzakhani's volume recursion, approach to WittenKontsevich theory by hyperbolic geometry, and prime simple geodesic theorem.
Lectures begin with a summary of the geometry of hyperbolic surfaces and approaches to the deformation theory of hyperbolic surfaces. General expositions are included on the geometry and topology of the moduli space of Riemann surfaces, the \(CAT(0)\) geometry of the augmented Teichmüller space, measured geodesic and ending laminations, the deformation theory of the prescribed curvature equation, and the Hermitian description of Riemann tensor. New material is included on estimating orbit sums as an approach for the potential theory of surfaces.
A copublication of the AMS and CBMS.
Graduate students and research mathematicians interested in Riemann surfaces, moduli spaces of Riemann surfaces, and Teichmüller theory.

Chapters

Chapter 1. Preliminaries

Chapter 2. Teichmüller space and horizontal strip deformations

Chapter 3. Geodesiclengths, twists and symplectic geometry

Chapter 4. Geometry of the augmented Teichmüller space, part 1

Chapter 5. Geometry of the augmented Teichmüller space, part 2

Chapter 6. Geometry of the augmented Teichmüller space, part 3

Chapter 7. Deformations of hyperbolic metrics and the curvature tensor

Chapter 8. Collar expansions and exponentialdistance sums

Chapter 9. Train tracks and the Mirzakhani volume recursion

Chapter 10. Mirzakhani prime simple geodesic theorem

...this book is that it introduces some topics that are at the frontier of current research, which are not discussed in other books on moduli spaces of Riemann surfaces. This book will be a good reference for researchers working in the field as well as those that just want to take a glimpse of the interconnection between different aspects of Teichmüller theory.
Mathematical Reviews 
[The author] takes pains to present a good deal of guidance as regards the indicated research literature and, indeed, each chapter ends with a useful recommendation of further readings.
Michael Berg, MAA Online