Teichmuller Theory And Quadratic Differentials

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Teichmüller Theory and Quadratic Differentials

Author : Frederick P. Gardiner
Publisher : Wiley-Interscience
ISBN 13 : 9780471845393
Total Pages : 256 pages
Book Rating : 4.8/5 (453 download)

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Book Synopsis Teichmüller Theory and Quadratic Differentials by : Frederick P. Gardiner

Download or read book Teichmüller Theory and Quadratic Differentials written by Frederick P. Gardiner and published by Wiley-Interscience. This book was released on 1987-08-11 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a unified treatment of both the modern and the classical aspects of Teichmuller theory. The classical parts of the theory include Teichmuller's theorem on the existence and uniqueness of an extremal quasiconformal mapping in a given homotopy class of mappings between Riemann surfaces, the theorems of Bers and Ahlfors on the completeness of Poincare theta series for general Fuchsian groups and the approximation of integrable holomorphic functions in a domain by rational functions with simple poles on the boundary of the domain. The modern aspects of the theory include Ahlfors's and Bers's natural complex analytic coordinates for Teichmuller space, the infinitesimal theory of Teichmuller's metric and Kobayashi's metric, Royden's theorem that the only biholomorphic self-mappings of Teichmuller's space are induced by elements of the modular group (the action of which group is discontinuous), the Hamilton-Krushkal necessary condition for extremality, and Reich and Strebel's proof of sufficiency.

Quasiconformal Teichmuller Theory

Author : Frederick P. Gardiner
Publisher : American Mathematical Soc.
ISBN 13 : 0821819836
Total Pages : 396 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quasiconformal Teichmuller Theory by : Frederick P. Gardiner

Download or read book Quasiconformal Teichmuller Theory written by Frederick P. Gardiner and published by American Mathematical Soc.. This book was released on 2000 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 up-to-date 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 three-dimensional manifolds through its relationship to Kleinian groups, and to one-dimensional dynamics through its relationship to quasisymmetric mappings. Many research problems in the application of function theory to geometry and dynamics are suggested.

Moduli Spaces of Riemann Surfaces

Author : Benson Farb
Publisher : American Mathematical Soc.
ISBN 13 : 0821898876
Total Pages : 371 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Moduli Spaces of Riemann Surfaces by : Benson Farb

Download or read book Moduli Spaces of Riemann Surfaces written by Benson Farb and published by American Mathematical Soc.. This book was released on 2013-08-16 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Handbook of Teichmüller Theory

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
ISBN 13 : 9783037190555
Total Pages : 888 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos

Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.

Teichmüller Theory in Riemannian Geometry

Author : Anthony Tromba
Publisher : Birkhäuser
ISBN 13 : 3034886136
Total Pages : 224 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Teichmüller Theory in Riemannian Geometry by : Anthony Tromba

Download or read book Teichmüller Theory in Riemannian Geometry written by Anthony Tromba and published by Birkhäuser. This book was released on 2012-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are based on the joint work of the author and Arthur Fischer on Teichmiiller theory undertaken in the years 1980-1986. Since then many of our colleagues have encouraged us to publish our approach to the subject in a concise format, easily accessible to a broad mathematical audience. However, it was the invitation by the faculty of the ETH Ziirich to deliver the ETH N achdiplom-Vorlesungen on this material which provided the opportunity for the author to develop our research papers into a format suitable for mathematicians with a modest background in differential geometry. We also hoped it would provide the basis for a graduate course stressing the application of fundamental ideas in geometry. For this opportunity the author wishes to thank Eduard Zehnder and Jiirgen Moser, acting director and director of the Forschungsinstitut fiir Mathematik at the ETH, Gisbert Wiistholz, responsible for the Nachdiplom Vorlesungen and the entire ETH faculty for their support and warm hospitality. This new approach to Teichmiiller theory presented here was undertaken for two reasons. First, it was clear that the classical approach, using the theory of extremal quasi-conformal mappings (in this approach we completely avoid the use of quasi-conformal maps) was not easily applicable to the theory of minimal surfaces, a field of interest of the author over many years. Second, many other active mathematicians, who at various times needed some Teichmiiller theory, have found the classical approach inaccessible to them.

The Complex Analytic Theory of Teichmuller Spaces

Author : Subhashis Nag
Publisher : Wiley-Interscience
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Complex Analytic Theory of Teichmuller Spaces by : Subhashis Nag

Download or read book The Complex Analytic Theory of Teichmuller Spaces written by Subhashis Nag and published by Wiley-Interscience. This book was released on 1988-03-03 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible, self-contained treatment of the complex structure of the Teichmüller moduli spaces of Riemann surfaces. Complex analysts, geometers, and especially string theorists (!) will find this work indispensable. The Teichmüller 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 Teichmüller spaces and deals with various types of complex-analytic coördinates 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 Teichmüller space is a complex analytic submersion. The fundamental universal property enjoyed by Teichmüller 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.

Teichmüller Theory and Applications to Geometry, Topology, and Dynamics

Author : John Hamal Hubbard
Publisher :
ISBN 13 : 9781943863013
Total Pages : 576 pages
Book Rating : 4.8/5 (63 download)

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Book Synopsis Teichmüller Theory and Applications to Geometry, Topology, and Dynamics by : John Hamal Hubbard

Download or read book Teichmüller Theory and Applications to Geometry, Topology, and Dynamics written by John Hamal Hubbard and published by . This book was released on 2022-02 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quadratic Differentials

Author : K. Strebel
Publisher : Springer Science & Business Media
ISBN 13 : 3662024144
Total Pages : 197 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Quadratic Differentials by : K. Strebel

Download or read book Quadratic Differentials written by K. Strebel and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quadratic differential on aRiemann surface is locally represented by a ho lomorphic function element wh ich transforms like the square of a derivative under a conformal change of the parameter. More generally, one also allows for meromorphic function elements; however, in many considerations it is con venient to puncture the surface at the poles of the differential. One is then back at the holomorphic case. A quadratic differential defines, in a natural way, a field of line elements on the surface, with singularities at the critical points, i.e. the zeros and poles of the differential. The integral curves of this field are called the trajectories of the differential. A large part of this book is about the trajectory structure of quadratic differentials. There are of course local and global aspects to this structure. Be sides, there is the behaviour of an individual trajectory and the structure deter mined by entire subfamilies of trajectories. An Abelian or first order differential has an integral or primitive function is in general not single-valued. In the case of a quadratic on the surface, which differential, one first has to take the square root and then integrate. The local integrals are only determined up to their sign and arbitrary additive constants. However, it is this multivalued function which plays an important role in the theory; the trajectories are the images of the horizontals by single valued branches of its inverse.

Handbook of Teichmüller Theory

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
ISBN 13 : 9783037190296
Total Pages : 812 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos

Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.

Teichmüller Theory and Applications to Geometry, Topology, and Dynamics

Author : John H. Hubbard
Publisher :
ISBN 13 : 9780971576629
Total Pages : 490 pages
Book Rating : 4.5/5 (766 download)

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Book Synopsis Teichmüller Theory and Applications to Geometry, Topology, and Dynamics by : John H. Hubbard

Download or read book Teichmüller Theory and Applications to Geometry, Topology, and Dynamics written by John H. Hubbard and published by . This book was released on 2006 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Teichmüller Theory

Author : Athanase Papadopoulos
Publisher :
ISBN 13 : 9783037197035
Total Pages : pages
Book Rating : 4.1/5 (97 download)

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Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos

Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume of the Handbook of Teichmüller theory is divided into three parts. The first part contains surveys on various topics in Teichmüller theory, including the complex structure of Teichmüller space, the Deligne-Mumford compactification of the moduli space, holomorphic quadratic differentials, Kleinian groups, hyperbolic 3-manifolds and the ending lamination theorem, the universal Teichmüller space, barycentric extensions of maps of the circle, and the theory of Higgs bundles. The second part consists of three historico-geometrical articles on Tissot (a precursor of the theory of quasiconfomal mappings), Grö̈tzsch and Lavrentieff, the two main founders of the modern theory of quasiconformal mappings. The third part comprises English translations of five papers by Grötzsch, a paper by Lavrentieff, and three papers by Teichmüller. These nine papers are foundational essays on the theories of conformal invariants and quasiconformal mappings, with applications to conformal geometry, to the type problem and to Nevanlinna's theory. The papers are followed by commentaries that highlight the relations between them and between later works on the subject. These papers are not only historical documents; they constitute an invaluable source of ideas for current research in Teichmüller theory.

An Introduction to Teichmüller Spaces

Author : Yoichi Imayoshi
Publisher : Springer Science & Business Media
ISBN 13 : 4431681744
Total Pages : 291 pages
Book Rating : 4.4/5 (316 download)

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Book Synopsis An Introduction to Teichmüller Spaces by : Yoichi Imayoshi

Download or read book An Introduction to Teichmüller Spaces written by Yoichi Imayoshi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an easy and compact access to the theory of TeichmA1/4ller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. TeichmA1/4ller 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, TeichmA1/4ller 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 TeichmA1/4ller 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.

Univalent Functions and Teichmüller Spaces

Author : O. Lehto
Publisher : Springer Science & Business Media
ISBN 13 : 1461386527
Total Pages : 271 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Univalent Functions and Teichmüller Spaces by : O. Lehto

Download or read book Univalent Functions and Teichmüller Spaces written by O. Lehto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph grew out of the notes relating to the lecture courses that I gave at the University of Helsinki from 1977 to 1979, at the Eidgenossische Technische Hochschule Zurich in 1980, and at the University of Minnesota in 1982. The book presumably would never have been written without Fred Gehring's continuous encouragement. Thanks to the arrangements made by Edgar Reich and David Storvick, I was able to spend the fall term of 1982 in Minneapolis and do a good part of the writing there. Back in Finland, other commitments delayed the completion of the text. At the final stages of preparing the manuscript, I was assisted first by Mika Seppala and then by Jouni Luukkainen, who both had a grant from the Academy of Finland. I am greatly indebted to them for the improvements they made in the text. I also received valuable advice and criticism from Kari Astala, Richard Fehlmann, Barbara Flinn, Fred Gehring, Pentti Jarvi, Irwin Kra, Matti Lehtinen, I1ppo Louhivaara, Bruce Palka, Kurt Strebel, Kalevi Suominen, Pekka Tukia and Kalle Virtanen. To all of them I would like to express my gratitude. Raili Pauninsalo deserves special thanks for her patience and great care in typing the manuscript. Finally, I thank the editors for accepting my text in Springer-Verlag's well known series. Helsinki, Finland June 1986 Olli Lehto Contents Preface. ... v Introduction ...

Quasiconformal Maps and Teichmüller Theory

Author : Alastair Fletcher
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Quasiconformal Maps and Teichmüller Theory by : Alastair Fletcher

Download or read book Quasiconformal Maps and Teichmüller Theory written by Alastair Fletcher and published by Oxford University Press, USA. This book was released on 2007 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description

The Teichmüller Theory of Harmonic Maps

Author : Michael Wolf
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Teichmüller Theory of Harmonic Maps by : Michael Wolf

Download or read book The Teichmüller Theory of Harmonic Maps written by Michael Wolf and published by . This book was released on 1986 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Primer on Mapping Class Groups

Author : Benson Farb
Publisher : Princeton University Press
ISBN 13 : 0691147949
Total Pages : 490 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis A Primer on Mapping Class Groups by : Benson Farb

Download or read book A Primer on Mapping Class Groups written by Benson Farb and published by Princeton University Press. This book was released on 2012 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Compact Riemann Surfaces

Author : Jürgen Jost
Publisher : Springer Science & Business Media
ISBN 13 : 3662034468
Total Pages : 304 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Compact Riemann Surfaces by : Jürgen Jost

Download or read book Compact Riemann Surfaces written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.