Publication Date
2025
Document Type
Dissertation/Thesis
First Advisor
Fletcher, Alastair N.
Degree Name
Ph.D. (Doctor of Philosophy)
Legacy Department
Department of Mathematical Sciences
Abstract
"
Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this dissertation we investigate three questions in this setting. The first is to show that quasiconformality and quasisymmetry with respect to the quasihyperbolic metric are equivalent. The second is to study normal quasiregular maps from such a domain into $S^n$ or $\mathbb{R}^n$ and determine they hold geometric properties such as a uniform Hölder condition. The third is to study preimages of a power-type mapping and show they are well-distributed in a precise sense.
Recommended Citation
Hahn, Allyson Mackenzie, "Geometric Function Theory on Uniformly Quasiconformally Homogeneous Domains" (2025). Graduate Research Theses & Dissertations. 8158.
https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/8158
Extent
137 pages
Language
en
Publisher
Northern Illinois University
Rights Statement
In Copyright
Rights Statement 2
NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.
Media Type
Text
