Quasihomographies in the theory of Teichmüller spaces

Zając Józef. Quasihomographies in the theory of Teichmüller spaces. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1996. <http://eudml.org/doc/270067>.

@book{ZającJózef1996,
abstract = {CONTENTSIntroduction............................................................................................................................5   I. Special functions of quasiconformal theory.....................................................................10      1. Introduction.................................................................................................................10      2. The distortion function $Φ_K$.....................................................................................11      3. Quasisymmetric functions............................................................................................19      4. Functional identities for special functions....................................................................27      5. Applications..................................................................................................................38   II. Quasihomographies of a circle.......................................................................................42      1. Introduction..................................................................................................................42      2. Introduction to quasihomographies..............................................................................42      3. Quasihomographies and quasisymmetric functions on the real line.............................45      4. Quasihomographies and quasisymmetric functions on the unit circle...........................48      5. Quasisymmetric functions as quasihomographies.........................................................51   III. Distortion theorems for quasihomographies....................................................................57      1. Introduction...................................................................................................................57      2. Similarities.....................................................................................................................57      3. Distortion theorems.......................................................................................................60      4. Normal and compact families of quasihomographies.....................................................67      5. Topological characterization of quasihomographies.......................................................69   IV. Quasihomographies of a Jordan curve ...........................................................................72      1. Introduction...................................................................................................................72      2. Harmonic cross-ratio.....................................................................................................72      3. One-dimensional quasiconformal mappings..................................................................76      4. Complete boundary transformations.............................................................................78      5. Quasicircles...................................................................................................................80   V. The universal Teichmüller space.......................................................................................84      1. Introduction....................................................................................................................84      2. The universal Teichmüller space of a circle...................................................................85      3. The universal Teichmüller space of an oriented Jordan curve........................................87      4. The space of normalized quasihomographies................................................................91      5. A linearization formula....................................................................................................94Acknowledgements...................................................................................................................97References...............................................................................................................................981991 Mathematics Subject Classification: 32H10, 42B10, 32A07, 46E22.},
author = {Zając Józef},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Quasihomographies in the theory of Teichmüller spaces},
url = {http://eudml.org/doc/270067},
year = {1996},
}

TY - BOOK
AU - Zając Józef
TI - Quasihomographies in the theory of Teichmüller spaces
PY - 1996
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction............................................................................................................................5   I. Special functions of quasiconformal theory.....................................................................10      1. Introduction.................................................................................................................10      2. The distortion function $Φ_K$.....................................................................................11      3. Quasisymmetric functions............................................................................................19      4. Functional identities for special functions....................................................................27      5. Applications..................................................................................................................38   II. Quasihomographies of a circle.......................................................................................42      1. Introduction..................................................................................................................42      2. Introduction to quasihomographies..............................................................................42      3. Quasihomographies and quasisymmetric functions on the real line.............................45      4. Quasihomographies and quasisymmetric functions on the unit circle...........................48      5. Quasisymmetric functions as quasihomographies.........................................................51   III. Distortion theorems for quasihomographies....................................................................57      1. Introduction...................................................................................................................57      2. Similarities.....................................................................................................................57      3. Distortion theorems.......................................................................................................60      4. Normal and compact families of quasihomographies.....................................................67      5. Topological characterization of quasihomographies.......................................................69   IV. Quasihomographies of a Jordan curve ...........................................................................72      1. Introduction...................................................................................................................72      2. Harmonic cross-ratio.....................................................................................................72      3. One-dimensional quasiconformal mappings..................................................................76      4. Complete boundary transformations.............................................................................78      5. Quasicircles...................................................................................................................80   V. The universal Teichmüller space.......................................................................................84      1. Introduction....................................................................................................................84      2. The universal Teichmüller space of a circle...................................................................85      3. The universal Teichmüller space of an oriented Jordan curve........................................87      4. The space of normalized quasihomographies................................................................91      5. A linearization formula....................................................................................................94Acknowledgements...................................................................................................................97References...............................................................................................................................981991 Mathematics Subject Classification: 32H10, 42B10, 32A07, 46E22.
LA - eng
UR - http://eudml.org/doc/270067
ER -