Handbook of Teichmüller Theory, Volume IV
| Autor: | Hideki Miyachi |
|---|---|
| Přispěvatelé: | Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2014 |
| Předmět: |
Weil-Petersson Funk metric
Teichmüller space Extremal length compactification affine structure quasiconformal map Lipschitz algebra Geometry Toledo invariant curve complex Thurston metric holomorphic dynamics deformation space Thurston boundary [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] Tits building Bers boundary Teichmüller theory Physics operad holomorphic family Teichmüller curve infinite-dimensional Teichmüller space horofunction boundary arc complex reduced Bers boundary Weil-Petersson metric Riemann surface moduli space universal curve 30-00 32-00 57-00 32G15 30F30 30F60 |
| Zdroj: | IRMA Lectures in Mathematics and Theoretical Physics ISBN: 9783037191170 Handbook of Teichmüller Theory, Volume IV France. European Mathematical Society, 838 p., 2014, 978-3-03719-117-0. ⟨10.4171/117⟩ |
| Popis: | International audience; Teichmüller theory is today one of the most active research areas in mathematics, with a very wide range of applications, including Riemann surface theory, hyperbolic geometry, low-dimensional topology, several complex variables, algebraic geometry, arithmetic, partial differential equations, dynamical systems, representation theory, symplectic geometry, geometric group theory and mathematical physics. This multi-volume set arose from an attempt to present the various aspects of the theory with its relations to all the other research fields. The present volume, Number IV in the series, is divided into five parts, namely: Part A: "The metric and the analytic theory, 4." Part B: "Representation theory and generalized structures, 2." Part C: "Dynamics" Part D: "The quantum theory, 2" Part E: "Sources"; Parts A, B and D are sequels of parts carrying the same name in previous volumes of this handbook. Part E , entitled "Sources", has a new character in the series; it contains the translation together with a commentary of an important paper by Teichmüller which is almost unknown even to specialists of the subject. We hope that rendering available this translation together with its commentary will give an impulse to new ideas in the theory and will help putting the theory in a broader perspective. Most of the chapters are expository, and written by experts who have a broad view on the theory, but several chapters also contain new and important results. Together with all the other subjects that were treated in the previous volumes, this constitutes an overview of quite a large number of beautiful ideas. The topics presented in this volume involve several areas of mathematics and I do not exclude any other area in future volumes. The volume contains surveys on the Weil-Petersson metric, on the geometry of simple closed curves on surfaces, on the curve complex and on its relations to buildings, on the arc complex and the related operad structure, on extremal length, on holomorphic families, on various boundary structures, on infinite dimensional Teichmüller spaces, on moduli spaces of affine structures, on higher Teichmüller theory, on quasi-conformal mappings in higher dimensions, on the Teichmüller theory of theory of iterations of rational maps of the sphere, on the dynamics of the mapping class group actions on Teichmüller spaces of surfaces of infinite type and on the quantization theory. |
| Databáze: | OpenAIRE |
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