The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps:
Saved in:
| Main Author: | |
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| Format: | Thesis Electronic eBook |
| Language: | English |
| Published: |
Passau
2016
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| Subjects: | |
| Online Access: | https://nbn-resolving.org/urn:nbn:de:bvb:739-opus4-3587 http://d-nb.info/1099702283/34 Volltext Inhaltsverzeichnis |
| Physical Description: | vi, 87 Seiten |
| Format: | Langzeitarchivierung gewährleistet, LZA |
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| 245 | 1 | 0 | |a The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps |c Sabrina Lehner |
| 264 | 1 | |a Passau |c 2016 | |
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| 653 | |a Riemann mapping theorem | ||
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Record in the Search Index
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| adam_text | Contents
Acknowledgements i
Notation v
1 Introduction 1
1.1 Motivation .............................................................. 1
1.2 Outline and Research Contributions....................................... 4
2 Preliminaries 9
2.1 Basic Definitions and Lemmas............................................. 9
2.2 The Riemann Mapping Theorem............................................. 15
2.3 Classification of Boundary Points....................................... 17
2.4 Asymptotic Behaviour at Analytically Regular Boundary Points ............19
2.4.1 Schwarz Reflection............................................... 19
2.4.2 General Premises................................................. 21
2.4.3 Asymptotic Behaviour............................................ 21
2.5 Asymptotic Behaviour at Analytic Corners .............................. 22
2.5.1 General Premises................................................. 23
2.5.2 Asymptotic Behaviour of the Mapping Function and its Inverse . . 24
2.5.3 Development in a Generalised Power Series....................... 25
2.6 O-minimal Structures ................................................... 27
2.6.1 Definitions ..................................................... 28
2.6.2 Examples......................................................... 30
2.6.3 O-minimal Content of the Riemann Mapping Theorem...............31
3 Asymptotic Behaviour at Analytic Cusps 33
3.1 General Premises........................................................34
3.2 Small Perturbation of Angles............................................37
3.3 Preliminary Transformation............................................. 38
3.4 Estimates for the Modulus and the Argument............................41
3.5 Asymptotic Behaviour of the Riemann map................................54
3.6 Asymptotic Behaviour of the Derivatives................................60
3.7 Asymptotic Behaviour of the Inverse.................................... 70
3.8 Asymptotic Behaviour of the Derivatives of the Inverse................72
4 Future Research 79
List of Figures 83
Bibliography 85
|
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| spelling | Lehner, Sabrina Verfasser aut The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps Sabrina Lehner Passau 2016 vi, 87 Seiten txt rdacontent c rdamedia cr rdacarrier Dissertation Universität Passau 2016 Langzeitarchivierung gewährleistet, LZA Riemannscher Abbildungssatz (DE-588)4178116-8 gnd rswk-swf Randverhalten (DE-588)4300459-3 gnd rswk-swf Geometrische Funktionentheorie (DE-588)4156711-0 gnd rswk-swf Riemann mapping theorem analytic cusp asymptotic behaviour boundary behaviour (DE-588)4113937-9 Hochschulschrift gnd-content Geometrische Funktionentheorie (DE-588)4156711-0 s Randverhalten (DE-588)4300459-3 s Riemannscher Abbildungssatz (DE-588)4178116-8 s DE-604 https://nbn-resolving.org/urn:nbn:de:bvb:739-opus4-3587 Resolving-System http://d-nb.info/1099702283/34 Langzeitarchivierung Nationalbibliothek https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/358 Verlag kostenfrei Volltext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029010624&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lehner, Sabrina The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps Riemannscher Abbildungssatz (DE-588)4178116-8 gnd Randverhalten (DE-588)4300459-3 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd |
| subject_GND | (DE-588)4178116-8 (DE-588)4300459-3 (DE-588)4156711-0 (DE-588)4113937-9 |
| title | The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps |
| title_auth | The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps |
| title_exact_search | The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps |
| title_full | The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps Sabrina Lehner |
| title_fullStr | The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps Sabrina Lehner |
| title_full_unstemmed | The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps Sabrina Lehner |
| title_short | The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps |
| title_sort | the asymptotic behaviour of the riemann mapping function at analytic cusps |
| topic | Riemannscher Abbildungssatz (DE-588)4178116-8 gnd Randverhalten (DE-588)4300459-3 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd |
| topic_facet | Riemannscher Abbildungssatz Randverhalten Geometrische Funktionentheorie Hochschulschrift |
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