| Title |
Handbook of Teichmüller Theory, Volume VII ([EBook] /) / Athanase Papadopoulos |
| Added Personal Name |
Papadopoulos, Athanase |
| Publication |
Zuerich, Switzerland : : European Mathematical Society Publishing House, , 2020 |
| Physical Details |
1 online resource (626 pages) |
| Series |
IRMA Lectures in Mathematics and Theoretical Physics (IRMA) 2523-5133 ; ; 30 |
| ISBN |
9783037197035 |
| Summary Note |
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 These papers are not only historical documents; they constitute an invaluable source of ideas for current research in Teichmüller theory.: |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 note |
Introduction to Teichmüller theory, old and new, VII /: The Deligne–Mumford compactification and crystallographic groups /: Complex geometry of Teichmüller domains /: Holomorphic quadratic differentials in Teichmüller theory /: Mostow strong rigidity of locally symmetric spaces revisited /: Models of ends of hyperbolic 3-manifolds. A survey /: Universal Teichmüller space as a non-trivial example of infinite-dimensional complex manifolds /: Generalized conformal barycentric extensions of circle maps /: Higgs bundles and higher Teichmüller spaces /: A note on Nicolas-Auguste Tissot: at the origin of quasiconformal mappings /: Memories of Herbert Grötzsch /: A note about Mikhaïl Lavrentieff and his world of analysis in the Soviet Union /: A letter /: On some extremal problems of the conformal mapping /: On some extremal problems of the conformal mapping II /: On the distortion of schlicht non-conformal mappings and on a related extension of Picard’s theorem /: On the distortion of non-conformal schlicht mappings of multiply-connected schlicht regions /: On closest-to-conformal mappings /: On five papers by Herbert Grötzsch /: On a class of continuous representations /: A commentary on Lavrentieff’s paper "Sur une classe de représentations continues" /: An application of quasiconformal mappings to the type problem /: Investigations on conformal and quasiconformal mappings /: Simple examples for value distribution /: Teichmüller’s work on the type problem /: A Commentary on Teichmüller’s paper "Untersuchungen über konforme und quasikonforme Abbildungen" /: Value distribution theory and Teichmüller’s paper "Einfache Beispiele zur Wertverteilungslehre" /: |
| Mode of acces to digital resource |
Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.4171/203 |
| See Also |
https://www.ems-ph.org/img/books/papadopoulos-vii_mini.jpg |
| Links to Related Works |
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