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An introduction to quasi-conformal mappings

Moosa, Leith Akil LU (2025) In Bachelor's Theses in Mathematical Sciences FMAL01 20242
Mathematics (Faculty of Engineering)
Abstract
This thesis introduces the theory of quasiconformal mappings on the plane. We give three different definitions of quasiconformal mappings: Differentiable quasiconformal map and two geometric definitions, one based on boundedness of the modulus of quadrilaterals and the other on ring domains. We also showcase when these definitions are equivalent. Then we prove that the geometric definition for quasiconformality is a local behaviour. Additionally we include some extension theorems for quasiconformal mappings, and end by proving Mori's Theorem.
Please use this url to cite or link to this publication:
author
Moosa, Leith Akil LU
supervisor
organization
course
FMAL01 20242
year
type
M2 - Bachelor Degree
subject
keywords
Mathematics, Mathematical analysis, Dynamical systems, Quasiconformal mappings
publication/series
Bachelor's Theses in Mathematical Sciences
report number
LUTFMA-4016-2025
ISSN
1654-6229
other publication id
2025:K29
language
English
id
9210761
date added to LUP
2025-09-15 11:20:15
date last changed
2025-09-15 13:22:20
@misc{9210761,
  abstract     = {{This thesis introduces the theory of quasiconformal mappings on the plane. We give three different definitions of quasiconformal mappings: Differentiable quasiconformal map and two geometric definitions, one based on boundedness of the modulus of quadrilaterals and the other on ring domains. We also showcase when these definitions are equivalent. Then we prove that the geometric definition for quasiconformality is a local behaviour. Additionally we include some extension theorems for quasiconformal mappings, and end by proving Mori's Theorem.}},
  author       = {{Moosa, Leith Akil}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor's Theses in Mathematical Sciences}},
  title        = {{An introduction to quasi-conformal mappings}},
  year         = {{2025}},
}