Quasihomographies in the theory of Teichmüller spaces

Zając Józef

GDML_Books, (1996), p.

Résumé

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...............................................................................................................................98

1991 Mathematics Subject Classification: 32H10, 42B10, 32A07, 46E22.

Détail

Zbl 0877.30021

EUDML-ID : urn:eudml:doc:270067