Functionals of finite Riemann surfaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton University Press
1954
|
| Series: | Princeton Mathematical Series
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 451 Seiten |
Staff View
MARC
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| 245 | 1 | 0 | |a Functionals of finite Riemann surfaces |c by Menahem Schiffer and Donald C. Spencer |
| 264 | 1 | |a Princeton, NJ |b Princeton University Press |c 1954 | |
| 300 | |a X, 451 Seiten | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Page
Chapter 1. Geometrical and physical considerations ... 1
1.1 Conformal flatness. Beltrami s equation .... 1
1.2 Exterior differential forms 11
1.3 Differential forms on Riemann surfaces. ... 15
1.4 Elementary topology of surfaces 17
1.5 Integration formulas 20
Chapter 2. Existence theorems for finite Riemann surfaces . 25
2.1 Definition of a Riemann surface 25
2.2 The double of a finite Riemann surface ... 29
2.3 Hilbert space 33
2.4 Orthogonal projection 40
2.5 The fundamental lemma 42
2.6 The existence of harmonic differentials with prescribed
periods 44
2.7 Existence of single valued harmonic functions with
singularities 48
2.8 Boundary value problems by the method of ortho¬
gonal projection . 51
2.9 Harmonic functions of a finite surface .... 58
2.10 The Uniformization Principle for finite surfaces . 59
2.11 Conformal mapping onto canonical domains of
higher genus 62
Chapter 3. Relations between differentials 64
3.1 Abelian differentials 64
3.2 The period matrix 71
3.3 Normalized differentials 72
3.4 Period relations 74
3.5 The order of a differential 76
3.6 The Riemann Roch theorem for finite Riemann
surfaces 78
3.7 Conformal mappings of a finite Riemann surface onto
itself 83
3.8 Reciprocal and quadratic differentials .... 85
Chapter 4. Bilinear differentials 88
4.1 Bilinear differentials and reproducing kernels . . 88
4.2 Definition of the Green s and Neumann s functions 93
4.3 Differentials of the first kind defined in terms of the
Green s function 101
viii
Page
4.4 Differentials of the first kind defined in terms of the
Neumann s function 105
4.5 Period matrices 107
4.6 Relations between the Green s and Neumann s func¬
tions 109
4.7 Canonical mapping functions 110
4.8 Classes of differentials 114
4.9 The bilinear differentials for the class F . . . 117
4.10 Construction of the bilinear differential for the class
M in terms of the Green s function 121
4.11 Construction of the bilinear differential for the class F 126
4.12 Properties of the bilinear differentials .... 129
4.13 Approximation of differentials 137
4.14 A special complete orthonormal system . . . 138
Chapter 5. Surfaces imbedded in a given surface .... 143
5.1 One surface imbedded in another 143
5.2 Several surfaces imbedded in a given surface . . 147
5.3 Fundamental identities 148
5.4 Inequalities for quadratic and Hermitian forms . 153
5.5 Extension of a local complex analytic imbedding of
one surface in another 158
5.6 Applications to schlicht functions 168
5.7 Extremal mappings 173
5.8 Non schlicht mappings 178
Chapter 6. Integral operators 181
6.1 Definition of the operators T, T and S . . . 181
6.2 Scalar products of transforms . . . . . . 185
6.3 The iterated operators 189
6.4 Spaces of piecewise analytic differentials . . . 198
6.5 Conditions for the vanishing of a differential . . 199
6.6 Bounds for the operators T and f 208
6.7 Spectral theory of the ^ operator 212
6.8 Spectral theory of the J operator 219
6.9 Spectral theory of the s operator 223
6.10 Minimum maximum properties of the eigen differen
tials 230
6.11 The Hilbert space with Dirichlet metric ... 233
6.12 Comparison with classical potential theory. . . 241
6.13 Relation between the eigen differentials of 9K and
3? — 3R 244
6.14 Extension to disconnected surfaces 252
6.15 Representation of domain functionals of 9Ji in terms
of the domain functionals of SR 254
ix
Page
6.16 The combination theorem 262
Chapter 7. Variations of surfaces and of their functionals . 273
7.1 Boundary variations 273
7.2 Variation of functionals as first terms of series
developments 277
7.3 Variation by cutting a hole 283
7.4 Variation by cutting a hole in a closed surface . 290
7.5 Attaching a handle to a closed surface .... 293
7.6 Attaching a handle to a surface with boundary . 299
7.7 Attaching a cross cap 303
7.8 Interior deformation by attaching a cell. First method 310
7.9 Interior deformation by attaching a cell. Second
method 314
7.10 The variation kernel 316
7.11 Identities satisfied by the variation kernel. . . 323
7.12 Conditions for conformal equivalence under a defor¬
mation 331
7.13 Construction of the variation which preserves con
formal type 334
7.14 Variational formulas for conformal mapping . . 347
7.15 Variations of boundary type 354
Chapter 8. Applications of the variational method .... 357
8.1 Identities for functionals 357
8.2 The coefficient problem for schlicht functions . . 364
8.3 Imbedding a circle in a given surface .... 376
8.4 Canonical cross cuts on a surface SR 385
8.5 Extremum problems in the conformal mapping of
plane domains 396
Chapter 9. Remarks on generalization to higher dimensional
Kahler manifolds 408
9.1 Kahler manifolds 408
9.2 Complex operators 415
9.3 Finite manifolds 420
9.4 Currents 423
9.5 Hermitian metrics 425
9.6 Dirichlet s principle for the real operators. . . 425
9.7 Bounded manifolds 433
9.8 Dirichlet s principle for the complex operators . 438
9.9 Bounded Kahler manifolds 439
9.10 Existence theorems on compact Kahler manifolds 440
9.11 The ^ kernels on finite Kahler manifolds . . . 443
9.12 Intrinsic definition of the operators 445
Index 448
X
|
| any_adam_object | 1 |
| author | Schiffer, Menahem 1911-1997 Spencer, Donald C. 1912-2001 |
| author_GND | (DE-588)1026135087 (DE-588)14004812X |
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| author_sort | Schiffer, Menahem 1911-1997 |
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| dewey-full | 517.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517.5 |
| dewey-search | 517.5 |
| dewey-sort | 3517.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002755935 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:49:10Z |
| institution | BVB |
| language | English |
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| physical | X, 451 Seiten |
| psigel | HUB-ZB011201106 |
| publishDate | 1954 |
| publishDateSearch | 1954 |
| publishDateSort | 1954 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Princeton Mathematical Series |
| series2 | Princeton Mathematical Series |
| spelling | Schiffer, Menahem 1911-1997 Verfasser (DE-588)1026135087 aut Functionals of finite Riemann surfaces by Menahem Schiffer and Donald C. Spencer Princeton, NJ Princeton University Press 1954 X, 451 Seiten txt rdacontent n rdamedia nc rdacarrier Princeton Mathematical Series 16 Riemann surfaces Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s DE-604 Spencer, Donald C. 1912-2001 Verfasser (DE-588)14004812X aut Princeton Mathematical Series 16 (DE-604)BV000019035 16 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001761742&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schiffer, Menahem 1911-1997 Spencer, Donald C. 1912-2001 Functionals of finite Riemann surfaces Princeton Mathematical Series Riemann surfaces Riemannsche Fläche (DE-588)4049991-1 gnd |
| subject_GND | (DE-588)4049991-1 |
| title | Functionals of finite Riemann surfaces |
| title_auth | Functionals of finite Riemann surfaces |
| title_exact_search | Functionals of finite Riemann surfaces |
| title_full | Functionals of finite Riemann surfaces by Menahem Schiffer and Donald C. Spencer |
| title_fullStr | Functionals of finite Riemann surfaces by Menahem Schiffer and Donald C. Spencer |
| title_full_unstemmed | Functionals of finite Riemann surfaces by Menahem Schiffer and Donald C. Spencer |
| title_short | Functionals of finite Riemann surfaces |
| title_sort | functionals of finite riemann surfaces |
| topic | Riemann surfaces Riemannsche Fläche (DE-588)4049991-1 gnd |
| topic_facet | Riemann surfaces Riemannsche Fläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001761742&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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