A survey on classical minimal surface theory:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Soc.
2012
|
| Series: | University lecture series
60 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | X, 182 S. graph. Darst. |
| ISBN: | 9780821869123 |
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| 245 | 1 | 0 | |a A survey on classical minimal surface theory |c William H. Meeks III ; Joaquín Pérez |
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| 650 | 7 | |a Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces |2 msc | |
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Record in the Search Index
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| adam_text | Titel: A survey on classical minimal surface theory
Autor: Meeks, William H
Jahr: 2012
Contents
Preface
1. Introduction
ix
2. Basic results in classical minimal surface theory 13
2.1. Eight equivalent definitions of minimality 13
2.2. Weierstrass representation 17
2.3. Minimal surfaces of finite total curvature 19
2.4. Periodic minimal surfaces 20
2.5. Some interesting examples of complete minimal surfaces 22
2.6. Monotonicity formula and classical maximum principles 33
2.7. Ends of properly embedded minimal surfaces 35
2.8. Second Variation of area, index of stability and Jacobi
functions 37
2.9. Barrier constructions 41
3. Minimal surfaces with finite topology and more than one end 45
3.1. Classification results for embedded minimal surfaces of
finite total curvature 45
3.2. Constructing embedded minimal surfaces of finite total
curvature 48
4. Limits of embedded minimal surfaces without local area or
curvature bounds 53
4.1. Colding-Minicozzi theory 53
viü Contents
4.1.1. Main strategy of the proof of Theorem 4.1.3. 58
4.1.2. More details on the main strategy 59
4.2. Minimal laminations with isolated singularities 69
5. The structure of minimal laminations of M3 73
6. The Ordering Theorem for the space of ends 77
7. Conformal structure of minimal surfaces 81
7.1. Recurrence and parabolicity for manifolds 81
7.2. Universal superharmonic functions 84
7.3. Quadratic area growth and middle ends 86
8. Uniqueness of the helicoid I: Proper case 91
9. Embedded minimal annular ends with infinite total curvature 95
9.1. Harmonie functions on annuli 95
9.2. Annular minimal ends of infinite total curvature 97
10. The embedded Calabi-Yau problem 103
10.1. Uniqueness ofthe helicoid II: Complete case 103
10.2. Regularity of the Singular set of convergence of a limit
minimal lamination 106
11. Local pictures, local removable singularities and dynamics 113
12. Embedded minimal surfaces of finite genus 123
12.1. The Hoffman-Meeks conjeeture 123
12.2. Non-existence of one-limit-ended examples 125
12.3. Uniqueness of the Riemann minimal examples 128
12.4. Colding-Minicozzi theory (fixed genus) 133
13. Topological aspects of minimal surfaces 137
14. Partial results on the Liouville Conjeeture 145
15. The Scherk Uniqueness Theorem 149
16. Calabi-Yau problems 153
17. Outstanding problems and conjeetures 157
Bibliography 171
|
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| id | DE-604.BV040604901 |
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| indexdate | 2024-07-10T00:27:08Z |
| institution | BVB |
| isbn | 9780821869123 |
| language | English |
| lccn | 2012027046 |
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| physical | X, 182 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
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| publisher | American Mathematical Soc. |
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| series | University lecture series |
| series2 | University lecture series |
| spelling | Meeks, William H. 1947- Verfasser (DE-588)123452600 aut A survey on classical minimal surface theory William H. Meeks III ; Joaquín Pérez Providence, RI American Mathematical Soc. 2012 X, 182 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier University lecture series 60 Includes bibliographical references and index Minimal surfaces Differential geometry -- Classical differential geometry -- Minimal surfaces, surfaces with prescribed mean curvature msc Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces msc Differential geometry -- Global differential geometry -- Immersions (minimal, prescribed curvature, tight, etc.) msc Minimalfläche (DE-588)4127814-8 gnd rswk-swf Minimalfläche (DE-588)4127814-8 s DE-604 Pérez, Joaquín 1966- Verfasser (DE-588)1026066980 aut Erscheint auch als Online-Ausgabe 978-0-8218-9198-8 University lecture series 60 (DE-604)BV004153846 60 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025432584&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meeks, William H. 1947- Pérez, Joaquín 1966- A survey on classical minimal surface theory University lecture series Minimal surfaces Differential geometry -- Classical differential geometry -- Minimal surfaces, surfaces with prescribed mean curvature msc Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces msc Differential geometry -- Global differential geometry -- Immersions (minimal, prescribed curvature, tight, etc.) msc Minimalfläche (DE-588)4127814-8 gnd |
| subject_GND | (DE-588)4127814-8 |
| title | A survey on classical minimal surface theory |
| title_auth | A survey on classical minimal surface theory |
| title_exact_search | A survey on classical minimal surface theory |
| title_full | A survey on classical minimal surface theory William H. Meeks III ; Joaquín Pérez |
| title_fullStr | A survey on classical minimal surface theory William H. Meeks III ; Joaquín Pérez |
| title_full_unstemmed | A survey on classical minimal surface theory William H. Meeks III ; Joaquín Pérez |
| title_short | A survey on classical minimal surface theory |
| title_sort | a survey on classical minimal surface theory |
| topic | Minimal surfaces Differential geometry -- Classical differential geometry -- Minimal surfaces, surfaces with prescribed mean curvature msc Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces msc Differential geometry -- Global differential geometry -- Immersions (minimal, prescribed curvature, tight, etc.) msc Minimalfläche (DE-588)4127814-8 gnd |
| topic_facet | Minimal surfaces Differential geometry -- Classical differential geometry -- Minimal surfaces, surfaces with prescribed mean curvature Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces Differential geometry -- Global differential geometry -- Immersions (minimal, prescribed curvature, tight, etc.) Minimalfläche |
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