On some aspects of oscillation theory and geometry
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2013
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| Schriftenreihe: | Memoirs of the American Mathematical Society
1056 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a On some aspects of oscillation theory and geometry |c Bruno Bianchini ; Luciano Mari ; Marco Rigoli |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2013 | |
| 300 | |a V, 195 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 1056 | |
| 500 | |a Volume 225, Number 1056 (first of 4 numbers) | ||
| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804151363988357120 |
|---|---|
| adam_text | Titel: On some aspects of oscillation theory and geometry
Autor: Bianchini, Bruno
Jahr: 2013
Contents
Chapter 1. Introduction 1
Chapter 2. The Geometric setting 7
2.1. Cut-locus and volume growth function 7
2.2. Model manifolds and basic comparisons 16
2.3. Some spectral theory on manifolds 29
Chapter 3. Some geometric examples related to oscillation theory 41
3.1. Conjugate points and Myers type compactness results 41
3.2. The spectrum of the Laplacian on complete manifolds 49
3.3. Spectral estimates and immersions 56
3.4. Spectral estimates and nonlinear PDE 60
Chapter 4. On the solutions of the ODE (vz ) + Avz = 0 69
4.1. Existence, uniqueness and the behaviour of zeroes 69
4.2. The critical curve: definition and main estimates 74
Chapter 5. Below the critical curve 87
5.1. Positivity and estimates from below 87
5.2. Stability, index of —A — q(x) and the uncertainty principle 93
5.3. A comparison at infinity for nonlinear PDE 101
5.4. Yamabe type equations with a sign-changing nonlinearity 108
5.5. Upper bounds for the number of zeroes of z 116
Chapter 6. Exceeding the critical curve 121
6.1. First zero and oscillation 121
6.2. Comparison with known criteria 127
6.3. Instability and index of —A — q(x) 130
6.4. Some remarks on minimal surfaces 132
6.5. Newton operators, unstable hypersurfaces and the Gauss map 140
6.6. Dealing with a possibly negative potential 151
6.7. An extension of Calabi compactness criterion 153
Chapter 7. Much above the critical curve 163
7.1. Controlling the oscillation 163
7.2. The growth of the index of —A — q(x) 178
7.3. The essential spectrum of —A and punctured manifolds 179
Bibliography 187
|
| any_adam_object | 1 |
| author | Bianchini, Bruno 1958- Mari, Luciano 1983- Rigoli, Marco 1955- |
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| format | Book |
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| id | DE-604.BV041296899 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:53:38Z |
| institution | BVB |
| isbn | 9780821887998 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026745768 |
| oclc_num | 862804715 |
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| physical | V, 195 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Bianchini, Bruno 1958- Verfasser (DE-588)1041942044 aut On some aspects of oscillation theory and geometry Bruno Bianchini ; Luciano Mari ; Marco Rigoli Providence, RI American Math. Soc. 2013 V, 195 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 1056 Volume 225, Number 1056 (first of 4 numbers) Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 s Elliptische Differentialgleichung (DE-588)4014485-9 s DE-604 Mari, Luciano 1983- Verfasser (DE-588)1041942176 aut Rigoli, Marco 1955- Verfasser (DE-588)1027715524 aut Memoirs of the American Mathematical Society 1056 (DE-604)BV008000141 1056 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026745768&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bianchini, Bruno 1958- Mari, Luciano 1983- Rigoli, Marco 1955- On some aspects of oscillation theory and geometry Memoirs of the American Mathematical Society Elliptische Differentialgleichung (DE-588)4014485-9 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4116561-5 |
| title | On some aspects of oscillation theory and geometry |
| title_auth | On some aspects of oscillation theory and geometry |
| title_exact_search | On some aspects of oscillation theory and geometry |
| title_full | On some aspects of oscillation theory and geometry Bruno Bianchini ; Luciano Mari ; Marco Rigoli |
| title_fullStr | On some aspects of oscillation theory and geometry Bruno Bianchini ; Luciano Mari ; Marco Rigoli |
| title_full_unstemmed | On some aspects of oscillation theory and geometry Bruno Bianchini ; Luciano Mari ; Marco Rigoli |
| title_short | On some aspects of oscillation theory and geometry |
| title_sort | on some aspects of oscillation theory and geometry |
| topic | Elliptische Differentialgleichung (DE-588)4014485-9 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Elliptische Differentialgleichung Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026745768&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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