@phdthesis{Pohl2019, author = {Pohl, Daniel}, title = {Universal Locally Univalent Functions and Universal Conformal Metrics}, doi = {10.25972/OPUS-17717}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-177174}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2019}, abstract = {The work at hand discusses various universality results for locally univalent and conformal metrics. In Chapter 2 several interesting approximation results are discussed. Runge-type Theorems for holomorphic and meromorphic locally univalent functions are shown. A well-known local approximation theorem for harmonic functions due to Keldysh is generalized to solutions of the curvature equation. In Chapter 3 and 4 these approximation theorems are used to establish universality results for locally univalent functions and conformal metrics. In particular locally univalent analogues for well-known universality results due Birkhoff, Seidel \& Walsh and Heins are shown.}, subject = {Schlichte Funktion}, language = {en} }