Compact Riemann surfaces: an introduction to contemporary mathematics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Edition: | 2. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 278 S. graph. Darst. |
| ISBN: | 354043299X |
Staff View
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| 245 | 1 | 0 | |a Compact Riemann surfaces |b an introduction to contemporary mathematics |c Jürgen Jost |
| 250 | |a 2. ed. | ||
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Record in the Search Index
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| adam_text | Table of Contents
Preface VII
1. Topological Foundations 1
1.1 Manifolds and Differentiable Manifolds 1
1.2 Homotopy of Maps. The Fundamental Group 3
1.3 Coverings 7
1.4 Global Continuation of Functions on Simply Connected
Manifolds 16
2. Differential Geometry of Riemann Surfaces 19
2.1 The Concept of a Riemann Surface 19
2.2 Some Simple Properties of Riemann Surfaces 22
2.3 Metrics on Riemann Surfaces 23
2.3. A Triangulations of Compact Riemann Surfaces 34
2.4 Discrete Groups of Hyperbolic Isometries. Fundamental
Polygons. Some Basic Concepts of Surface Topology and
Geometry 41
2.4.A The Topological Classification of Compact Riemann
Surfaces 55
2.5 The Theorems of Gauss Bonnet and Riemann Hurwitz .... 59
2.6 A General Schwarz Lemma 66
2.7 Conformal Structures on Tori 74
3. Harmonic Maps 81
3.1 Review: Banach and Hilbert Spaces. The Hilbert Space L2 . 81
3.2 The Sobolev Space W1 2 = H1 2 93
3.3 The Dirichlet Principle. Weak Solutions of the Poisson
Equation 102
3.4 Harmonic and Subharmonic Functions 106
3.5 The Ca Regularity Theory 113
3.6 Maps Between Surfaces. The Energy Integral. Definition
and Simple Properties of Harmonic Maps 120
3.7 Existence of Harmonic Maps 126
3.8 Regularity of Harmonic Maps 135
XVI Table of Contents
3.9 Uniqueness of Harmonic Maps 140
3.10 Harmonic Diffeomorphisms 145
3.11 Metrics and Conformal Structures 154
4. Teichmiiller Spaces 161
4.1 The Basic Definitions 161
4.2 Harmonic Maps, Conformal Structures and Holomorphic
Quadratic Differentials. Teichmiiller s Theorem 164
4.3 Fenchel Nielsen Coordinates. An Alternative Approach to
the Topology of Teichmiiller Space 174
4.4 Uniformization of Compact Riemann Surfaces 184
5. Geometric Structures on Riemann Surfaces 189
5.1 Preliminaries: Cohomology and Homology Groups 189
5.2 Harmonic and Holomorphic Differential Forms on Riemann
Surfaces 197
5.3 The Periods of Holomorphic and Meromorphic Differential
Forms 205
5.4 Divisors. The Riemann Roch Theorem 211
5.5 Holomorphic 1 Forms and Metrics on Compact Riemann
Surfaces 222
5.6 Divisors and Line Bundles 224
5.7 Projective Embeddings 234
5.8 Algebraic Curves 242
5.9 Abel s Theorem and the Jacobi Inversion Theorem 254
5.10 Elliptic Curves 262
Sources and References 269
Bibliography 271
Index of Notation 273
Index 275
|
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| discipline | Mathematik |
| edition | 2. ed. |
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| indexdate | 2024-07-09T19:00:15Z |
| institution | BVB |
| isbn | 354043299X |
| language | English German |
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| physical | XVI, 278 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Springer |
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| series2 | Universitext |
| spelling | Jost, Jürgen 1956- Verfasser (DE-588)115774564 aut Riemannsche Flächen Compact Riemann surfaces an introduction to contemporary mathematics Jürgen Jost 2. ed. Berlin [u.a.] Springer 2002 XVI, 278 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Riemann, Surfaces de Riemann-vlakken gtt Riemann surfaces Kompakte Riemannsche Fläche (DE-588)4164852-3 gnd rswk-swf Kompakte Riemannsche Fläche (DE-588)4164852-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009765713&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jost, Jürgen 1956- Compact Riemann surfaces an introduction to contemporary mathematics Riemann, Surfaces de Riemann-vlakken gtt Riemann surfaces Kompakte Riemannsche Fläche (DE-588)4164852-3 gnd |
| subject_GND | (DE-588)4164852-3 |
| title | Compact Riemann surfaces an introduction to contemporary mathematics |
| title_alt | Riemannsche Flächen |
| title_auth | Compact Riemann surfaces an introduction to contemporary mathematics |
| title_exact_search | Compact Riemann surfaces an introduction to contemporary mathematics |
| title_full | Compact Riemann surfaces an introduction to contemporary mathematics Jürgen Jost |
| title_fullStr | Compact Riemann surfaces an introduction to contemporary mathematics Jürgen Jost |
| title_full_unstemmed | Compact Riemann surfaces an introduction to contemporary mathematics Jürgen Jost |
| title_short | Compact Riemann surfaces |
| title_sort | compact riemann surfaces an introduction to contemporary mathematics |
| title_sub | an introduction to contemporary mathematics |
| topic | Riemann, Surfaces de Riemann-vlakken gtt Riemann surfaces Kompakte Riemannsche Fläche (DE-588)4164852-3 gnd |
| topic_facet | Riemann, Surfaces de Riemann-vlakken Riemann surfaces Kompakte Riemannsche Fläche |
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