Handbook of Teichmüller Theory, Volume VII / Athanase Papadopoulos

Format:

Book

Author/Creator:

Papadopoulos, Athanase, editor.

Contributor:

Papadopoulos, Athanase, editor.

Series:

IRMA Lectures in Mathematics and Theoretical Physics (IRMA) ; 30

IRMA Lectures in Mathematics and Theoretical Physics (IRMA) ; 2523-5133 ; 30

Language:

English

Subjects (All):

Teichmüller spaces.

Functional analysis.

Functions of complex variables.

Geometry, Algebraic.

Several complex variables and analytic spaces.

Dynamical systems and ergodic theory.

Local Subjects:

Several complex variables and analytic spaces.

Dynamical systems and ergodic theory.

Physical Description:

1 online resource (626 pages)

Place of Publication:

Zuerich, Switzerland : European Mathematical Society Publishing House, 2020

Zürich, Switzerland : European Mathematical Society Publishing House, 2020.

Language Note:

English

System Details:

text file PDF

Summary:

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), Grötzsch 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 These papers are not only historical documents; they constitute an invaluable source of ideas for current research in Teichmüller theory.

Contents:

Introduction to Teichmüller theory, old and new, VII /; Athanase Papadopoulos

; The Deligne-Mumford compactification and crystallographic groups /; Yukio Matsumoto

; Complex geometry of Teichmüller domains /; Subhojoy Gupta, Harish Seshadri

; Holomorphic quadratic differentials in Teichmüller theory /; Subhojoy Gupta

; Mostow strong rigidity of locally symmetric spaces revisited /; Lizhen Ji

; Models of ends of hyperbolic 3-manifolds. A survey /; Mahan Mj

; Universal Teichmüller space as a non-trivial example of infinite-dimensional complex manifolds /; Armen Sergeev

; Generalized conformal barycentric extensions of circle maps /; Jun Hu

; Higgs bundles and higher Teichmüller spaces /; Óscar García Prada

; A note on Nicolas-Auguste Tissot: at the origin of quasiconformal mappings /; Athanase Papadopoulos

; Memories of Herbert Grötzsch /; Reiner Kühnau

; A note about Mikhaïl Lavrentieff and his world of analysis in the Soviet Union /; Athanase Papadopoulos, Galina Sinkevich

; A letter /; Oswald Teichmüller

; On some extremal problems of the conformal mapping /; Herbert Grötzsch

; On some extremal problems of the conformal mapping II /; Herbert Grötzsch

; On the distortion of schlicht non-conformal mappings and on a related extension of Picard's theorem /; Herbert Grötzsch

; On the distortion of non-conformal schlicht mappings of multiply-connected schlicht regions /; Herbert Grötzsch

; On closest-to-conformal mappings /; Herbert Grötzsch

; On five papers by Herbert Grötzsch /; Vincent Alberge, Athanase Papadopoulos

; On a class of continuous representations /; Mikhaïl Lavrentieff

; A commentary on Lavrentieff's paper "Sur une classe de représentations continues" /; Vincent Alberge, Athanase Papadopoulos

; An application of quasiconformal mappings to the type problem /; Oswald Teichmüller

; Investigations on conformal and quasiconformal mappings /; Oswald Teichmüller

; Simple examples for value distribution /; Oswald Teichmüller

; Teichmüller's work on the type problem /; Vincent Alberge, Melkana Brakalova-Trevithick, Athanase Papadopoulos

; A Commentary on Teichmüller's paper "Untersuchungen über konforme und quasikonforme Abbildungen" /; Vincent Alberge, Melkana Brakalova-Trevithick, Athanase Papadopoulos

; Value distribution theory and Teichmüller's paper "Einfache Beispiele zur Wertverteilungslehre" /; Athanase Papadopoulos.

ISBN:

3-03719-703-X