Geometry and spectra of compact Riemann surfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston, Mass. ; Basel ; Berlin
Birkhäuser
1992
|
| Series: | Progress in Mathematics
106 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 454 Seiten graph. Darst. |
| ISBN: | 0817634061 3764334061 |
Staff View
MARC
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| 100 | 1 | |a Buser, Peter |d 1946- |e Verfasser |0 (DE-588)142814288 |4 aut | |
| 245 | 1 | 0 | |a Geometry and spectra of compact Riemann surfaces |c Peter Buser |
| 264 | 1 | |a Boston, Mass. ; Basel ; Berlin |b Birkhäuser |c 1992 | |
| 300 | |a XIV, 454 Seiten |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
Chapter 1
Hyperbolic Structures 1
1.1 The Hyperbolic Plane 1
1.2 Hyperbolic Structures 5
1.3 Pasting 8
1.4 The Universal Covering 15
1.5 Perpendiculars 17
1.6 Closed Geodesies 21
1.7 The Fenchel Nielsen Parameters 27
Chapter 2
Trigonometry 31
2.1 The Hyperboloid Model 31
2.2 Triangles 33
2.3 Trirectanglcs and Pentagons 37
2.4 Hexagons 40
2.5 Variable Curvature 43
2.6 Appendix: The Hyperboloid Model Revisited 49
The Quaternion Model 49
A Trace Relation 55
The General Sine and Cosine Formula 57
Chapter 3
Y Pieces and Twist Parameters 63
3.1 Y Pieces 63
3.2 Marked Y Pieces 67
3.3 Twist Parameters 69
3.4 Signature (1,1) 76
3.5 Cubic Graphs 78
3.6 The Compact Riemann Surfaces 81
xii Contents
3.7 Appendix: The Length Spectrum Is of Unbounded Multiplicity 84
Geometric Approach 85
Algebraic Approach 89
Chapter 4
The Collar Theorem 94
4.1 Collars 94
4.2 Non Simple Closed Geodesies 98
4.3 Variable Curvature 104
4.4 Cusps 108
4.5 Triangulations of Controlled Size 116
Chapter 5
Bers Constant and the Hairy Torus 122
5.1 Bers Theorem 123
5.2 Partitions 124
5.3 The Hairy Torus 130
5.4 Bers1 Constant Without Curvature Bounds 133
Chapter 6
The Teichmuller Space 138
6.1 Marked Riemann Surfaces 138
6.2 Models of Teichmuller Space 142
6.3 The Real Analytic Structure of I3g 147
6.4 Distances in STg 152
6.5 The Teichmuller Modular Group 154
6.6 A Rough Fundamental Domain 160
6.7 The Coordinates of Zieschang Vogt Coldewey 164
6.8 Fuchsian Groups and Bers Coordinates 170
Chapter 7
The Spectrum of the Laplacian 182
7.1 Introduction 182
7.2 The Spectrum and the Heat Equation 184
7.3 The Abel Transform 194
7.4 The Heat Kernel of the Hyperbolic Plane 197
7.5 The Heat Kernel of T H 205
Chapter 8
Small Eigenvalues 210
8.1 The Interval [0, ] 210
8.2 The Minimax Principles 213
8.3 Cheeger s Inequality 215
8.4 Eigenvalue Estimates 218
Contents xiii
Chapter 9
Closed Geodesies and Huber s Theorem 224
9.1 The Origin of the Length Spectrum 225
9.2 Summation over the Lengths 227
9.3 Summation over the Eigenvalues 235
9.4 The Prime Number Theorem 241
9.5 Selberg s Trace Formula 252
9.6 The Prime Number Theorem with Error Terms 256
9.7 Lattice Points 261
Chapter 10
Wolpert s Theorem 268
10.1 Introduction 268
10.2 Curve Systems 270
10.3 Finitely Many Lengths Determine the Length Spectrum 273
10.4 Generic Surfaces Are Determined by Their Spectrum 275
10.5 Decoding the Moduli 278
Chapter 11
Sunada s Theorem 283
11.1 Some History 283
11.2 Examples of Almost Conjugate Groups 285
11.3 Proof of Sunada s Theorem 291
11.4 Cay ley Graphs 296
11.5 Transplantation of Eigenfunctions 304
11.6 Transplantation of Closed Geodesies 307
Chapter 12
Examples of Isospectral Riemann Surfaces 311
12.1 Cayley Graphs and Hyperbolic Polygons 311
12.2 Smoothness 313
12.3 Examples over ZJ * Z8 318
12.4 Examples over SL(3, 2) 321
12.5 Genus 6 325
12.6 Large Families 332
12.7 Criteria For Non Isometry 333
Chapter 13
The Size of Isospectral Families 340
13.1 Finiteness 340
13.2 Parameter Geodesies of Length exp( 4g) 344
13.3 Measuring the Twist Parameters 347
13.4 Parameter Geodesies of Length exp( 4g) 355
xiv Contents
Chapter 14
Perturbations of the Laplacian in Hilbert Space 362
14.1 The Hilbert Spaces Ho and Hl 362
14.2 The Friedrichs Extension of the Laplacian 366
14.3 A Representation Theorem 370
14.4 Resolvents and Projectors 373
14.5 Holomorphic Families 380
14.6 A Model of Teichmuller Space 382
14.7 Reduction to Finite Dimension 388
14.8 Holomorphic Families of Laplacians 397
14.9 Analytic Properties of the Eigenvalues 399
14.10 Finite Parts of the Spectrum 406
Appendix
Curves and Isotopies 409
The Theorems of Baer Epstein Zieschang 409
An Application to the 3 Holed Sphere 424
Length Decreasing Homotopies 428
Bibliography 433
Index 448
Glossary 454
|
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| illustrated | Illustrated |
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| institution | BVB |
| isbn | 0817634061 3764334061 |
| language | English |
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| physical | XIV, 454 Seiten graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Birkhäuser |
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| series | Progress in Mathematics |
| series2 | Progress in Mathematics |
| spelling | Buser, Peter 1946- Verfasser (DE-588)142814288 aut Geometry and spectra of compact Riemann surfaces Peter Buser Boston, Mass. ; Basel ; Berlin Birkhäuser 1992 XIV, 454 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in Mathematics 106 Kompakte Riemannsche Fläche (DE-588)4164852-3 gnd rswk-swf Laplace-Operator (DE-588)4166772-4 gnd rswk-swf Kompakte Riemannsche Fläche (DE-588)4164852-3 s DE-604 Laplace-Operator (DE-588)4166772-4 s Progress in Mathematics 106 (DE-604)BV000004120 106 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003681715&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buser, Peter 1946- Geometry and spectra of compact Riemann surfaces Progress in Mathematics Kompakte Riemannsche Fläche (DE-588)4164852-3 gnd Laplace-Operator (DE-588)4166772-4 gnd |
| subject_GND | (DE-588)4164852-3 (DE-588)4166772-4 |
| title | Geometry and spectra of compact Riemann surfaces |
| title_auth | Geometry and spectra of compact Riemann surfaces |
| title_exact_search | Geometry and spectra of compact Riemann surfaces |
| title_full | Geometry and spectra of compact Riemann surfaces Peter Buser |
| title_fullStr | Geometry and spectra of compact Riemann surfaces Peter Buser |
| title_full_unstemmed | Geometry and spectra of compact Riemann surfaces Peter Buser |
| title_short | Geometry and spectra of compact Riemann surfaces |
| title_sort | geometry and spectra of compact riemann surfaces |
| topic | Kompakte Riemannsche Fläche (DE-588)4164852-3 gnd Laplace-Operator (DE-588)4166772-4 gnd |
| topic_facet | Kompakte Riemannsche Fläche Laplace-Operator |
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