Harmonic mappings in the plane:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
|
| Ausgabe: | 1. publication |
| Schriftenreihe: | Cambridge Tracts in Mathematics
156 |
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index. |
| Beschreibung: | XII, 212 Seiten graph. Darst. |
| ISBN: | 0521641217 |
Internformat
MARC
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| 100 | 1 | |a Duren, Peter L. |d 1935-2020 |e Verfasser |0 (DE-588)135675502 |4 aut | |
| 245 | 1 | 0 | |a Harmonic mappings in the plane |c Peter Duren, University of Michigan |
| 250 | |a 1. publication | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2004 | |
| 300 | |a XII, 212 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Cambridge Tracts in Mathematics |v 156 | |
| 500 | |a Includes bibliographical references and index. | ||
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| 650 | 7 | |a Harmonische functies |2 gtt | |
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Datensatz im Suchindex
| _version_ | 1804130160126984192 |
|---|---|
| adam_text | Contents
Preface page xi
1 Preliminaries 1
1.1 Harmonic Mappings 1
1.2 Some Basic Facts 3
1.3 The Argument Principle 7
1.4 The Dirichlet Problem 11
1.5 Conformal Mappings 13
1.6 Overview of Harmonic Mapping Theory 16
2 General Properties of Harmonic Mappings 18
2.1 Critical Points of Harmonic Functions 18
2.2 Lewy s Theorem 20
2.3 Heinz s Lemma 21
2.4 Rado s Theorem 23
2.5 Counterexamples in Higher Dimensions 25
2.6 Approximation Theorem 27
3 Harmonic Mappings onto Convex Regions 29
3.1 The Rado Kneser Choquet Theorem 29
3.2 Choquet s Proof 31
3.3 Boundary Behavior 34
3.4 The Shear Construction 36
3.5 Structure of Convex Mappings 45
3.6 Covering Theorems and Coefficient Bounds 48
3.7 Failure of the Rado Kneser Choquet Theorem in R3 54
4 Harmonic Self Mappings of the Disk 57
4.1 Representation by Rado Kneser Choquet Theorem 57
4.2 Mappings onto Regular Polygons 59
4.3 Arbitrary Convex Polygons 62
4.4 Sharp Form of Heinz s Inequality 66
vii
viii Contents
4.5 Coefficient Estimates 72
4.6 Schwarz s Lemma for Harmonic Mappings 75
5 Harmonic Univalent Functions 78
5.1 Normalizations 78
5.2 Normal Families 79
5.3 The Harmonic Koebe Function 82
5.4 Coefficient Conjectures 86
6 Extremal Problems 89
6.1 Minimum Area 89
6.2 Covering Theorems 90
6.3 Estimation of | ^21 95
6.4 Growth and Distortion 97
6.5 Marty Relation 101
6.6 Typically Real Functions 103
6.7 Starlike Functions 106
7 Mapping Problems 111
7.1 Generalized Riemann Mapping Theorem 111
7.2 Collapsing 112
7.3 Concavity of the Boundary 115
7.4 Angles at Corners 118
7.5 Existence Theorems 126
7.6 Proof of Existence 129
7.7 Uniqueness Problem 133
8 Additional Topics 136
8.1 Harmonic Mappings of Annuli 136
8.2 Multiply Connected Domains 138
8.3 Inverse of a Harmonic Mapping 145
8.4 Decomposition of Harmonic Functions 149
8.5 Integral Means 151
9 Minimal Surfaces 156
9.1 Background in Surface Theory 156
9.2 Isothermal Parameters 162
9.3 Weierstrass Enneper Representation 165
9.4 Some Examples 169
9.5 Historical Notes 172
10 Curvature of Minimal Surfaces 173
10.1 Gauss Curvature 173
10.2 Minimal Graphs and Harmonic Mappings 175
10.3 Heinz s Lemma and Bounds on Curvature 182
Contents ix
10.4 Sharp Bounds on Curvature 186
10.5 Schwarzian Derivatives 189
Appendix Extremal Length 196
References 201
Index 211
|
| any_adam_object | 1 |
| author | Duren, Peter L. 1935-2020 |
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| discipline | Mathematik |
| edition | 1. publication |
| format | Book |
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| id | DE-604.BV017321057 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:16:37Z |
| institution | BVB |
| isbn | 0521641217 |
| language | English |
| lccn | 2003056516 |
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| physical | XII, 212 Seiten graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge Tracts in Mathematics |
| series2 | Cambridge Tracts in Mathematics |
| spelling | Duren, Peter L. 1935-2020 Verfasser (DE-588)135675502 aut Harmonic mappings in the plane Peter Duren, University of Michigan 1. publication Cambridge Cambridge University Press 2004 XII, 212 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge Tracts in Mathematics 156 Includes bibliographical references and index. Applications harmoniques Harmonische functies gtt Potentiaaltheorie gtt Harmonic maps Ebene (DE-588)4150968-7 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 s Ebene (DE-588)4150968-7 s DE-604 Cambridge Tracts in Mathematics 156 (DE-604)BV000000001 156 http://www.loc.gov/catdir/description/cam032/2003056516.html Publisher description http://www.loc.gov/catdir/toc/cam032/2003056516.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duren, Peter L. 1935-2020 Harmonic mappings in the plane Cambridge Tracts in Mathematics Applications harmoniques Harmonische functies gtt Potentiaaltheorie gtt Harmonic maps Ebene (DE-588)4150968-7 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| subject_GND | (DE-588)4150968-7 (DE-588)4023452-6 |
| title | Harmonic mappings in the plane |
| title_auth | Harmonic mappings in the plane |
| title_exact_search | Harmonic mappings in the plane |
| title_full | Harmonic mappings in the plane Peter Duren, University of Michigan |
| title_fullStr | Harmonic mappings in the plane Peter Duren, University of Michigan |
| title_full_unstemmed | Harmonic mappings in the plane Peter Duren, University of Michigan |
| title_short | Harmonic mappings in the plane |
| title_sort | harmonic mappings in the plane |
| topic | Applications harmoniques Harmonische functies gtt Potentiaaltheorie gtt Harmonic maps Ebene (DE-588)4150968-7 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| topic_facet | Applications harmoniques Harmonische functies Potentiaaltheorie Harmonic maps Ebene Harmonische Abbildung |
| url | http://www.loc.gov/catdir/description/cam032/2003056516.html http://www.loc.gov/catdir/toc/cam032/2003056516.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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