Spectral geometry: direct and inverse problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1986
|
| Schriftenreihe: | Lecture notes in mathematics
1207 : Subseries: Instituto de Matemática Pura e Aplicada, Rio de Janeiro |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Weitere Ausgabe: Monografias de matemática ; 41 |
| Beschreibung: | XIII, 272 S. |
| ISBN: | 3540167889 0387167889 |
Internformat
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| 100 | 1 | |a Bérard, Pierre H. |d 1949- |e Verfasser |0 (DE-588)102644411 |4 aut | |
| 245 | 1 | 0 | |a Spectral geometry |b direct and inverse problems |c Pierre H. Bérard. With an appendix by G. Besson |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1986 | |
| 300 | |a XIII, 272 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1207 : Subseries: Instituto de Matemática Pura e Aplicada, Rio de Janeiro | |
| 500 | |a Weitere Ausgabe: Monografias de matemática ; 41 | ||
| 650 | 4 | |a Opérateurs, Théorie des | |
| 650 | 4 | |a Riemann, Géométrie de | |
| 650 | 4 | |a Valeurs propres | |
| 650 | 4 | |a Eigenvalues | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Spectral geometry | |
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Laplace-Beltrami-Operator |0 (DE-588)4451064-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| adam_text |
CONTENTS '
CHAPTER I
MOTIVATIONS AND THE PHYSICAL POINT OF VIEW
A An elementary example: The vibrating string 1
B The method of separation of variables 8
C Generalization: The vibrating membrane 10
D Other points of view: Partial differential equations vs
Spectral theory 14
CHAPTER II
TOPICS FROM RIEMANNIAN GEOMETRY
A Generalities 21
B Curvatures: The geometric point of view 27
C The covariant derivative 35
D Curvatures: The analytic point of view 39
CHAPTER III
THE LAPLACIAN AND RELATED TOPICS
A Starring: The Laplacian and the Rayleigh quotient 44
B Eigenvalue problems on Riemannian manifolds I:
variational characterization of eigenvalues 52
C Eigenvalue problems on Riemannian manifolds II:
applications 64
CHAPTER IV
ISOPERIMETRIC METHODS
A Motivations: The Faber-Krahn inequality 78
B Isoperimetric inequalities and symmetrization 84
. The isoperimetric function of a closed Riemannian manifold. 84
. Symmetrization 86
. Applications 90
(1) Numbers refer to pages
XI
CHAPTER V
ISOPERIMETRIC METHODS AND THE HEAT EQUATION
A The heat kernel 98
B Isoperimetric inequality for the heat kernel I:
main theorem 101
C Isoperimetric inequality for the heat kernel II:
an effective case 108
D Applications 112
CHAPTER VI
GEOMETRIC APPLICATIONS OF ISOPERIMETRIC METHODS
A Introduction 116
B The analytic approach I 118
. Bochner vanishing theorems 118
. Generalized Bochner vanishing theorems 126
C The analytic approach II 129
D The analytic approach III: Estimating theorems 134
E Underlying philosophy: M. Gromov's compactness theorems 139
CHAPTER VII
A BRIEF SURVEY OF SOME RECENT DEVELOPMENTS IN SPECTRAL GEOMETRY
A The heat equation and applications 145
. The isospectral problem 147
B The wave equation and applications 149
C Final comments 153
APPENDIX A by G. BESSON
ON SYMMETRIZATION
Introduction 156
The absolute value as a symmetrization procedure and
the Beurling-Denys criterion 159
Symmetrization 163
Interpretation in terms of quadratic forms:
a criterion for semi-group domination 168
Application 1: Kato's inequality on fibre bundles 172
Application 2: Schwarz symmetrization 175
References for Appendix A 190
XII
APPENDIX B by P. BgRARD and M. BERGER
A GUIDE TO THE LITERATURE
"Le spectre d'une variete riemannienne en 1982" 192
APPENDIX C
A COMPLEMENT TO APPENDIX B 249
REFERENCES
. References for Chapters I to VII 257
INDEXES
. Subject index 265
Index of notations 270
XIII |
| any_adam_object | 1 |
| author | Bérard, Pierre H. 1949- |
| author_GND | (DE-588)102644411 |
| author_facet | Bérard, Pierre H. 1949- |
| author_role | aut |
| author_sort | Bérard, Pierre H. 1949- |
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| building | Verbundindex |
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| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| classification_tum | MAT 536f |
| ctrlnum | (OCoLC)610639981 (DE-599)BVBBV000527343 |
| dewey-full | 516.3/73 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry 510 - Mathematics |
| dewey-raw | 516.3/73 510 |
| dewey-search | 516.3/73 510 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV000527343 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T04:38:28Z |
| institution | BVB |
| isbn | 3540167889 0387167889 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000325228 |
| oclc_num | 610639981 |
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| physical | XIII, 272 S. |
| psigel | TUB-nvmb |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Bérard, Pierre H. 1949- Verfasser (DE-588)102644411 aut Spectral geometry direct and inverse problems Pierre H. Bérard. With an appendix by G. Besson Berlin [u.a.] Springer 1986 XIII, 272 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1207 : Subseries: Instituto de Matemática Pura e Aplicada, Rio de Janeiro Weitere Ausgabe: Monografias de matemática ; 41 Opérateurs, Théorie des Riemann, Géométrie de Valeurs propres Eigenvalues Operator theory Spectral geometry Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Laplace-Beltrami-Operator (DE-588)4451064-0 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Eigenwert (DE-588)4151200-5 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 s Geometrie (DE-588)4020236-7 s DE-604 Laplace-Beltrami-Operator (DE-588)4451064-0 s Eigenwert (DE-588)4151200-5 s Lecture notes in mathematics 1207 : Subseries: Instituto de Matemática Pura e Aplicada, Rio de Janeiro (DE-604)BV000676446 1207 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000325228&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bérard, Pierre H. 1949- Spectral geometry direct and inverse problems Lecture notes in mathematics Opérateurs, Théorie des Riemann, Géométrie de Valeurs propres Eigenvalues Operator theory Spectral geometry Spektraltheorie (DE-588)4116561-5 gnd Laplace-Beltrami-Operator (DE-588)4451064-0 gnd Geometrie (DE-588)4020236-7 gnd Eigenwert (DE-588)4151200-5 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4451064-0 (DE-588)4020236-7 (DE-588)4151200-5 |
| title | Spectral geometry direct and inverse problems |
| title_auth | Spectral geometry direct and inverse problems |
| title_exact_search | Spectral geometry direct and inverse problems |
| title_full | Spectral geometry direct and inverse problems Pierre H. Bérard. With an appendix by G. Besson |
| title_fullStr | Spectral geometry direct and inverse problems Pierre H. Bérard. With an appendix by G. Besson |
| title_full_unstemmed | Spectral geometry direct and inverse problems Pierre H. Bérard. With an appendix by G. Besson |
| title_short | Spectral geometry |
| title_sort | spectral geometry direct and inverse problems |
| title_sub | direct and inverse problems |
| topic | Opérateurs, Théorie des Riemann, Géométrie de Valeurs propres Eigenvalues Operator theory Spectral geometry Spektraltheorie (DE-588)4116561-5 gnd Laplace-Beltrami-Operator (DE-588)4451064-0 gnd Geometrie (DE-588)4020236-7 gnd Eigenwert (DE-588)4151200-5 gnd |
| topic_facet | Opérateurs, Théorie des Riemann, Géométrie de Valeurs propres Eigenvalues Operator theory Spectral geometry Spektraltheorie Laplace-Beltrami-Operator Geometrie Eigenwert |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000325228&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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