Gromov's compactness theorem for pseudo-holomorphic curves:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | German |
| Published: |
Basel, [u.a.]
Birkhäuser
[1997]
|
| Series: | Progress in mathematics
151 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 131 Seiten Illustrationen |
| ISBN: | 3764357355 0817657355 |
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MARC
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| 100 | 1 | |a Hummel, Christoph |d 1928- |0 (DE-588)173595278 |4 aut | |
| 245 | 1 | 0 | |a Gromov's compactness theorem for pseudo-holomorphic curves |c Christoph Hummel |
| 264 | 1 | |a Basel, [u.a.] |b Birkhäuser |c [1997] | |
| 264 | 4 | |c © 1997 | |
| 300 | |a viii, 131 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 151 | |
| 502 | |b Diplomarbeit |c Universität Freiburg (Breisgau) |d 1992 | ||
| 650 | 7 | |a Applications holomorphes |2 ram | |
| 650 | 7 | |a Riemann, Surfaces de |2 ram | |
| 650 | 4 | |a Holomorphic mappings | |
| 650 | 4 | |a Riemann surfaces | |
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Record in the Search Index
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| adam_text |
Contents
Introduction 1
Chapter I Preliminaries
1. Riemannian manifolds 5
2. Almost complex and symplectic manifolds 7
3. 7 holomorphic maps 10
4. Riemann surfaces and hyperbolic geometry 11
5. Annuli 17
Chapter II Estimates for area and first derivatives
1. Gromov's Schwarz and monotonicity lemma 21
2. Area of y holomorphic maps 22
3. Isoperimetric inequalities for 7 holomorphic maps 23
4. Proof of the Gromov Schwarz lemma 30
Chapter III Higher order derivatives
1. 1 jets of 7 holomorphic maps 35
2. Removal of singularities 41
3. Converging sequences of y holomorphic maps 45
4. Variable almost complex structures 46
Chapter IV Hyperbolic surfaces
1. Hexagons 49
2. Building hyperbolic surfaces from pairs of pants 55
3. Pairs of pants decomposition 59
4. Thick thin decomposition 68
5. Compactness properties of hyperbolic structures 70
Chapter V The compactness theorem
1. Cusp curves 79
2. Proof of the compactness theorem 82
3. Bubbles 91
Chapter VI The squeezing theorem
1. Discussion of the statement 99
2. Proof modulo existence result for pseudo holomorphic curves 102
3. The analytical setup: A rough outline 104
4. The required existence result 110
viii Contents
Appendix A The classical isoperimetric inequality 115
Appendix B The C* topology 117
References on pseudo holomorphic curves 121
Bibliography 125
Index 129 |
| any_adam_object | 1 |
| author | Hummel, Christoph 1928- |
| author_GND | (DE-588)173595278 |
| author_facet | Hummel, Christoph 1928- |
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| author_sort | Hummel, Christoph 1928- |
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| classification_tum | MAT 325f MAT 306f |
| ctrlnum | (OCoLC)36767926 (DE-599)BVBBV011299483 |
| dewey-full | 516.3/73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/73 |
| dewey-search | 516.3/73 |
| dewey-sort | 3516.3 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-09-17T14:07:47Z |
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| isbn | 3764357355 0817657355 |
| language | German |
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| publishDate | 1997 |
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| spelling | Hummel, Christoph 1928- (DE-588)173595278 aut Gromov's compactness theorem for pseudo-holomorphic curves Christoph Hummel Basel, [u.a.] Birkhäuser [1997] © 1997 viii, 131 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 151 Diplomarbeit Universität Freiburg (Breisgau) 1992 Applications holomorphes ram Riemann, Surfaces de ram Holomorphic mappings Riemann surfaces Kompaktheit (DE-588)4456100-3 gnd rswk-swf Pseudoholomorphe Funktion (DE-588)4176138-8 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Riemannscher Raum (DE-588)4128295-4 s Symplektische Mannigfaltigkeit (DE-588)4290704-4 s Pseudoholomorphe Funktion (DE-588)4176138-8 s Kompaktheit (DE-588)4456100-3 s DE-604 Erscheint auch als Online-Ausgabe 978-3-0348-8952-0 Progress in mathematics 151 (DE-604)BV000004120 151 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007590220&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hummel, Christoph 1928- Gromov's compactness theorem for pseudo-holomorphic curves Progress in mathematics Applications holomorphes ram Riemann, Surfaces de ram Holomorphic mappings Riemann surfaces Kompaktheit (DE-588)4456100-3 gnd Pseudoholomorphe Funktion (DE-588)4176138-8 gnd Riemannscher Raum (DE-588)4128295-4 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd |
| subject_GND | (DE-588)4456100-3 (DE-588)4176138-8 (DE-588)4128295-4 (DE-588)4290704-4 (DE-588)4113937-9 |
| title | Gromov's compactness theorem for pseudo-holomorphic curves |
| title_auth | Gromov's compactness theorem for pseudo-holomorphic curves |
| title_exact_search | Gromov's compactness theorem for pseudo-holomorphic curves |
| title_full | Gromov's compactness theorem for pseudo-holomorphic curves Christoph Hummel |
| title_fullStr | Gromov's compactness theorem for pseudo-holomorphic curves Christoph Hummel |
| title_full_unstemmed | Gromov's compactness theorem for pseudo-holomorphic curves Christoph Hummel |
| title_short | Gromov's compactness theorem for pseudo-holomorphic curves |
| title_sort | gromov s compactness theorem for pseudo holomorphic curves |
| topic | Applications holomorphes ram Riemann, Surfaces de ram Holomorphic mappings Riemann surfaces Kompaktheit (DE-588)4456100-3 gnd Pseudoholomorphe Funktion (DE-588)4176138-8 gnd Riemannscher Raum (DE-588)4128295-4 gnd Symplektische Mannigfaltigkeit (DE-588)4290704-4 gnd |
| topic_facet | Applications holomorphes Riemann, Surfaces de Holomorphic mappings Riemann surfaces Kompaktheit Pseudoholomorphe Funktion Riemannscher Raum Symplektische Mannigfaltigkeit Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007590220&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT hummelchristoph gromovscompactnesstheoremforpseudoholomorphiccurves |