The complex analytic theory of Teichmüller spaces

Author: Subhashis Nag

Publisher: Wiley-Interscience


Category: Mathematics

Page: 427

View: 3480

An accessible, self-contained treatment of the complex structure of the Teichm?ller moduli spaces of Riemann surfaces. Complex analysts, geometers, and especially string theorists (!) will find this work indispensable. The Teichm?ller space, parametrizing all the various complex structures on a given surface, itself carries (in a completely natural way) the complex structure of a finite- or infinite-dimensional complex manifold. Nag emphasizes the Bers embedding of Teichm?ller spaces and deals with various types of complex-analytic co?rdinates for them. This is the first book in which a complete exposition is given of the most basic fact that the Bers projection from Beltrami differentials onto Teichm?ller space is a complex analytic submersion. The fundamental universal property enjoyed by Teichm?ller space is given two proofs and the Bers complex boundary is examined to the point where totally degenerate Kleinian groups make their spectacular appearance. Contains much material previously unpublished.

In the Tradition of Ahlfors-Bers, IV

Ahlfors-Bers Colloquium, May 19-22, 2005, University of Michigan, Ann Arbor, Michigan

Author: Richard Douglas Canary

Publisher: American Mathematical Soc.

ISBN: 0821842277

Category: Mathematics

Page: 229

View: 2403

The Ahlfors-Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmuller theory, hyperbolic manifolds, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields, such as algebraic geometry, mathematical physics, dynamics, geometric group theory, number theory, and topology. The triannual Ahlford-Bers colloquia serve as a venue to disseminate the relevant work to the wider mathematical community and bring the key participants together to ponder future directions in the field. The present volume includes a wide range of articles in the fields central to this legacy. The majority of articles present new results, but there are expository articles as well.

Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces

AMS Special Session in Honor of Clifford J. Earle, October 2-3, 2010, Syracuse University, Syracuse, New York

Author: Yunping Jiang,Sudeb Mitra

Publisher: American Mathematical Soc.

ISBN: 0821853406

Category: Mathematics

Page: 375

View: 3472

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.

Fully Nonlinear PDEs in Real and Complex Geometry and Optics

Cetraro, Italy 2012, Editors: Cristian E. Gutiérrez, Ermanno Lanconelli

Author: Luca Capogna,Pengfei Guan,Cristian E. Gutiérrez,Annamaria Montanari

Publisher: Springer

ISBN: 3319009427

Category: Mathematics

Page: 210

View: 307

The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari.

An Introduction to Teichmüller Spaces

Author: Yoichi Imayoshi,Masahiko Taniguchi

Publisher: Springer Science & Business Media

ISBN: 4431681744

Category: Mathematics

Page: 279

View: 9258

This book offers an easy and compact access to the theory of Teichmüller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. Teichmüller spaces give parametrization of all the complex structures on a given Riemann surface. This subject is related to many different areas of mathematics including complex analysis, algebraic geometry, differential geometry, topology in two and three dimensions, Kleinian and Fuchsian groups, automorphic forms, complex dynamics, and ergodic theory. Recently, Teichmüller spaces have begun to play an important role in string theory. Imayoshi and Taniguchi have attempted to make the book as self-contained as possible. They present numerous examples and heuristic arguments in order to help the reader grasp the ideas of Teichmüller theory. The book will be an excellent source of information for graduate students and reserachers in complex analysis and algebraic geometry as well as for theoretical physicists working in quantum theory.

Theorie Der Abel'schen Functionen: Erstes Heft

Author: Karl Weierstrass

Publisher: Wentworth Press

ISBN: 9780341642336

Category: History

Page: 108

View: 5597

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Foundations of P-adic Teichmüller Theory

Author: Shinichi Mochizuki

Publisher: American Mathematical Soc.

ISBN: 9780821888155

Category: Mathematics

Page: 529

View: 3835

This book lays the foundation for a theory of uniformization of $p$-adic hyperbolic curves and their moduli. On one hand, this theory generalizes the Fuchsian and Bers uniformizations of complex hyperbolic curves and their moduli to nonarchimedian places. That is why in this book, the theory is referred to as $p$-adic Teichmüller theory, for short. On the other hand, the theory may be regarded as a fairly precise hyperbolic analog of the Serre-Tate theory of ordinary abelian varieties and their moduli. The theory of uniformization of $p$-adic hyperbolic curves and their moduli was initiated in a previous work by Mochizuki. And in some sense, this book is a continuation and generalization of that work. This book aims to bridge the gap between the approach presented and the classical uniformization of a hyperbolic Riemann surface that is studied in undergraduate complex analysis.