Universal Locally Univalent Functions and Universal Conformal Metrics
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 th...
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| Format: | Doctoral Thesis |
| Language: | English |
| Published: |
2019
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| Online Access: | https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/17717 http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-177174 https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-177174 https://opus.bibliothek.uni-wuerzburg.de/files/17717/Pohl_Daniel_Dissertation.pdf |
| Summary: | 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. === In Kapitel 2 werden Runge-Sätze für holomorphe und meromorphe lokal schlichte Funktionen und ein lokaler Approximationsstaz für konforme Metriken mit negativer Krümmung bewiesen. Mithilfe dieser Sätze werden In Kapitel 3 und 4 Universalitätsresultate für lokal schlichte Funktionen und konforme Metriken gezeigt. |
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