@phdthesis{Biersack2024,
  author    = {Biersack, Florian},
  title     = {Topological Properties of Quasiconformal Automorphism Groups},
  doi       = {10.25972/OPUS-35917},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-359177},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2024},
  abstract  = {The goal of this thesis is to study the topological and algebraic properties of the quasiconformal automorphism groups of simply and multiply connected domains in the complex plain, in which the quasiconformal automorphism groups are endowed with the supremum metric on the underlying domain. More precisely, questions concerning central topological properties such as (local) compactness, (path)-connectedness and separability and their dependence on the boundary of the corresponding domains are studied, as well as completeness with respect to the supremum metric. Moreover, special subsets of the quasiconformal automorphism group of the unit disk are investigated, and concrete quasiconformal automorphisms are constructed. Finally, a possible application of quasiconformal unit disk automorphisms to symmetric cryptography is presented, in which a quasiconformal cryptosystem is defined and studied.},
  subject      = {Quasikonforme Abbildung},
  language  = {en}
}