Conformally Natural Extensions of Continuous Circle Maps

Title: Conformally Natural Extensions of Continuous Circle Maps
Identifier: d_2009_2013:dac4f09a4912:11341
identifier: 11699
Creator: Muzician, Oleg,
Contributor: Jun Hu
Date: 2012
Language: English
Publisher: City University of New York.
Subject: Mathematics | Applied mathematics | Complex Analysis | Conformally natural extesions | Douady-Earle extensions
Abstract: Conformally natural and continuous extensions were originally introduced by Douady and Earle for circle homeomorphisms, and later by Abikoff, Earle and Mitra for continuous degree +/-1 monotone circle maps. The first main result of this thesis shows that conformally natural and continuous extensions exist for all continuous circle maps. The second main result shows that if f is a continuous circle map and is M-quasisymmetric on some arc on the unit circle S1, then such an extension of f is locally K-quasiconformal on a neighborhood of the arc in the open unit disk D, where the neighborhood and K depend only on M.
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics