Universal Locally Univalent Functions and Universal Conformal Metrics
Universelle Lokal Schlichte Funktionen und Universelle Konforme Metriken
Please always quote using this URN: urn:nbn:de:bvb:20-opus-177174
- 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. InThe 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.
Author: | Daniel Pohl |
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URN: | urn:nbn:de:bvb:20-opus-177174 |
Document Type: | Doctoral Thesis |
Granting Institution: | Universität Würzburg, Fakultät für Mathematik und Informatik |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Referee: | Prof. Dr. Oliver Roth, Prof. Dr. Jürgen Müller |
Date of final exam: | 2019/02/15 |
Language: | English |
Year of Completion: | 2019 |
DOI: | https://doi.org/10.25972/OPUS-17717 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
GND Keyword: | Schlichte Funktion; Konforme Metrik |
Tag: | Conformal Metrics; Curvature Equation; Runge-type Theorems; Universal Functions |
Release Date: | 2019/03/06 |
Licence (German): | CC BY-NC-SA: Creative-Commons-Lizenz: Namensnennung, Nicht kommerziell, Weitergabe unter gleichen Bedingungen 4.0 International |