Teichm Ller Theory And Quadratic Differentials

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Teichm Ller Theory And Quadratic Differentials

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Author : Frederick P. Gardiner
language : en
Publisher: Wiley-Interscience
Release Date : 1987-08-11

Teichm Ller Theory And Quadratic Differentials written by Frederick P. Gardiner and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-08-11 with Mathematics categories.

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

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Author : Frederick P. Gardiner
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Quasiconformal Teichmuller Theory written by Frederick P. Gardiner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

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.

Teichm Ller Theory In Riemannian Geometry

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Author : Anthony Tromba
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Teichm Ller Theory In Riemannian Geometry written by Anthony Tromba and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Handbook Of Teichm Ller Theory

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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007

Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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.

The Complex Analytic Theory Of Teichmuller Spaces

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Author : Subhashis Nag
language : en
Publisher: Wiley-Interscience
Release Date : 1988-03-03

The Complex Analytic Theory Of Teichmuller Spaces written by Subhashis Nag and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-03-03 with Mathematics categories.

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.

Teichm Ller Theory And Applications To Geometry Topology And Dynamics

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Author : John H. Hubbard
language : en
Publisher:
Release Date : 2006

Teichm Ller Theory And Applications To Geometry Topology And Dynamics written by John H. Hubbard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

Handbook Of Teichm Ller Theory

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Author : Athanase Papadopoulos
language : en
Publisher:
Release Date : 2020

Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Teichmüller spaces categories.

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.

The Teichm Ller Theory Of Harmonic Maps

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Author : Michael Wolf
language : en
Publisher:
Release Date : 1986

The Teichm Ller Theory Of Harmonic Maps written by Michael Wolf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.

Quasiconformal Maps And Teichm Ller Theory

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Author : Alastair Fletcher
language : en
Publisher: Oxford University Press, USA
Release Date : 2007

Quasiconformal Maps And Teichm Ller Theory written by Alastair Fletcher and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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Moduli Spaces Of Riemann Surfaces

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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-16

Moduli Spaces Of Riemann Surfaces written by Benson Farb and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 with Mathematics categories.

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.