New complex analytic methods in the study of non-orientable minimal surfaces in Rn:
The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in for any . These methods, which we develop essentially from the first principles, enable us to prove that the space of conformal minimal immersio...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
March 2020
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| Series: | Memoirs of the American Mathematical Society
volume 264, number 1283 (sixth of 6 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in for any . These methods, which we develop essentially from the first principles, enable us to prove that the space of conformal minimal immersions of a given bordered non-orientable surface to is a real analytic Banach manifold (see Theorem 1.1), obtain approximation results of Runge-Mergelyan type for conformal minimal immersions from non-orientable surfaces (see Theorem 1.2 and Corollary 1.3), and show general position theorems for non-orientable conformal minimal surfaces in (see Theorem 1.4). We also give the first known example of a properly embedded non-orientable minimal surface in ; a Möbius strip (see Example 6.1).All our new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables us to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, we construct proper non-orientable conformal minimal surfaces in with any given conformal structure (see Theorem 1.6 (i)), complete non-orientable minimal surfaces in with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits hyperplanes of in general position (see Theorem 1.6 (iii)), complete non-orientable minimal surfaces bounded by Jordan curves (see Theorem 1.5), and complete proper non-orientable minimal surfaces normalized by bordered surfaces in -convex domains of (see Theorem 1.7). |
| Item Description: | Literaturverzeichnis: Seite 73-77 |
| Physical Description: | vi, 77 Seiten Illustrationen |
| ISBN: | 9781470441616 |
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| 245 | 1 | 0 | |a New complex analytic methods in the study of non-orientable minimal surfaces in Rn |c Antonio Alarcón, Franc Forstnerič, Francisco J. López |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 264, number 1283 (sixth of 6 numbers) | |
| 500 | |a Literaturverzeichnis: Seite 73-77 | ||
| 520 | |a The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in for any . These methods, which we develop essentially from the first principles, enable us to prove that the space of conformal minimal immersions of a given bordered non-orientable surface to is a real analytic Banach manifold (see Theorem 1.1), obtain approximation results of Runge-Mergelyan type for conformal minimal immersions from non-orientable surfaces (see Theorem 1.2 and Corollary 1.3), and show general position theorems for non-orientable conformal minimal surfaces in (see Theorem 1.4). We also give the first known example of a properly embedded non-orientable minimal surface in ; a Möbius strip (see Example 6.1).All our new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables us to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, we construct proper non-orientable conformal minimal surfaces in with any given conformal structure (see Theorem 1.6 (i)), complete non-orientable minimal surfaces in with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits hyperplanes of in general position (see Theorem 1.6 (iii)), complete non-orientable minimal surfaces bounded by Jordan curves (see Theorem 1.5), and complete proper non-orientable minimal surfaces normalized by bordered surfaces in -convex domains of (see Theorem 1.7). | ||
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Record in the Search Index
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| adam_text | American Mathematical Society
Number 1283
New Complex Analytic Methods in
the Study of Non-Orientable Minimal
Surfaces in Rn
Antonio Alarcön
Franc Forstneric
Francisco J Lopez
ULB Darmstadt
20396504
Universitäts- und
Landesbibliothek
Darmstadt
March 2020 • Volume 264 • Number 1283 (sixth of 6 numbers)
V
I • •
• ••a a a r American
A MATHEMATICAL
*-• 1 UVLJ SOCIETY
Contents
Chapter 1 Introduction 1
11A summary of the main results 1
1 2 Basic notions of minimal surface theory 3
1 3 Approximation and general position theorems 4
1 4 Complete non-orientable minimal surfaces with Jordan boundaries 7
1 5 Proper non-orientable minimal surfaces in domains in Rn 9
Chapter 2 Preliminaries 13
2 1 Conformal structures on surfaces 13
2 2 3-invariant functions and 1-forms Spaces of functions and maps 14
2 3 Homology basis and period map 16
2 4 Conformal minimal immersions of non-orientable surfaces 20
2 5 Notation 23
Chapter 3 Gluing 3-invariant sprays and applications 25
3 1 3-invariant sprays 25
3 2 Gluing 3-invariant sprays on 3-invariant Cartan pairs 27
3 3 3-invariant period dominating sprays 30
3 4 Banach manifold structure of the space CMI5 (A/) 31
3 5 Basic approximation results 35
3 6 The Riemann-Hilbert method for non-orientable minimal surfaces 37
Chapter 4 Approximation theorems for non-orientable minimal surfaces 41
41A Mergelyan approximation theorem 42
42A Mergelyan theorem with fixed components 48
Chapter 5 A general position theorem for non-orientable minimal surfaces 55
Chapter 6 Applications 59
6 1 Proper non-orientable minimal surfaces in Rn 59
6 2 Complete non-orientable minimal surfaces with fixed components 63
6 3 Complete non-orientable minimal surfaces with Jordan boundaries 68
6 4 Proper non-orientable minimal surfaces in p-convex domains 69
Bibliography 73
|
| adam_txt |
American Mathematical Society
Number 1283
New Complex Analytic Methods in
the Study of Non-Orientable Minimal
Surfaces in Rn
Antonio Alarcön
Franc Forstneric
Francisco J Lopez
ULB Darmstadt
20396504
Universitäts- und
Landesbibliothek
Darmstadt
March 2020 • Volume 264 • Number 1283 (sixth of 6 numbers)
V
I • •
• ••a a a r' American
A \ MATHEMATICAL
*-• 1 UVLJ SOCIETY
Contents
Chapter 1 Introduction 1
11A summary of the main results 1
1 2 Basic notions of minimal surface theory 3
1 3 Approximation and general position theorems 4
1 4 Complete non-orientable minimal surfaces with Jordan boundaries 7
1 5 Proper non-orientable minimal surfaces in domains in Rn 9
Chapter 2 Preliminaries 13
2 1 Conformal structures on surfaces 13
2 2 3-invariant functions and 1-forms Spaces of functions and maps 14
2 3 Homology basis and period map 16
2 4 Conformal minimal immersions of non-orientable surfaces 20
2 5 Notation 23
Chapter 3 Gluing 3-invariant sprays and applications 25
3 1 3-invariant sprays 25
3 2 Gluing 3-invariant sprays on 3-invariant Cartan pairs 27
3 3 3-invariant period dominating sprays 30
3 4 Banach manifold structure of the space CMI5 (A/) 31
3 5 Basic approximation results 35
3 6 The Riemann-Hilbert method for non-orientable minimal surfaces 37
Chapter 4 Approximation theorems for non-orientable minimal surfaces 41
41A Mergelyan approximation theorem 42
42A Mergelyan theorem with fixed components 48
Chapter 5 A general position theorem for non-orientable minimal surfaces 55
Chapter 6 Applications 59
6 1 Proper non-orientable minimal surfaces in Rn 59
6 2 Complete non-orientable minimal surfaces with fixed components 63
6 3 Complete non-orientable minimal surfaces with Jordan boundaries 68
6 4 Proper non-orientable minimal surfaces in p-convex domains 69
Bibliography 73 |
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| spelling | Alarcón, Antonio (DE-588)1213305063 aut New complex analytic methods in the study of non-orientable minimal surfaces in Rn Antonio Alarcón, Franc Forstnerič, Francisco J. López Providence, RI American Mathematical Society March 2020 vi, 77 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 264, number 1283 (sixth of 6 numbers) Literaturverzeichnis: Seite 73-77 The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in for any . These methods, which we develop essentially from the first principles, enable us to prove that the space of conformal minimal immersions of a given bordered non-orientable surface to is a real analytic Banach manifold (see Theorem 1.1), obtain approximation results of Runge-Mergelyan type for conformal minimal immersions from non-orientable surfaces (see Theorem 1.2 and Corollary 1.3), and show general position theorems for non-orientable conformal minimal surfaces in (see Theorem 1.4). We also give the first known example of a properly embedded non-orientable minimal surface in ; a Möbius strip (see Example 6.1).All our new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables us to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, we construct proper non-orientable conformal minimal surfaces in with any given conformal structure (see Theorem 1.6 (i)), complete non-orientable minimal surfaces in with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits hyperplanes of in general position (see Theorem 1.6 (iii)), complete non-orientable minimal surfaces bounded by Jordan curves (see Theorem 1.5), and complete proper non-orientable minimal surfaces normalized by bordered surfaces in -convex domains of (see Theorem 1.7). Holomorphie (DE-588)4160484-2 gnd rswk-swf Affiner Raum (DE-588)4141574-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Affiner Raum (DE-588)4141574-7 s Holomorphie (DE-588)4160484-2 s DE-604 Forstnerič, Franc 1958- (DE-588)1016469241 aut López, Francisco J. (DE-588)1213305365 aut Memoirs of the American Mathematical Society volume 264, number 1283 (sixth of 6 numbers) (DE-604)BV008000141 1283 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032237786&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alarcón, Antonio Forstnerič, Franc 1958- López, Francisco J. New complex analytic methods in the study of non-orientable minimal surfaces in Rn Memoirs of the American Mathematical Society Holomorphie (DE-588)4160484-2 gnd Affiner Raum (DE-588)4141574-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4160484-2 (DE-588)4141574-7 (DE-588)4012248-7 |
| title | New complex analytic methods in the study of non-orientable minimal surfaces in Rn |
| title_auth | New complex analytic methods in the study of non-orientable minimal surfaces in Rn |
| title_exact_search | New complex analytic methods in the study of non-orientable minimal surfaces in Rn |
| title_exact_search_txtP | New complex analytic methods in the study of non-orientable minimal surfaces in Rn |
| title_full | New complex analytic methods in the study of non-orientable minimal surfaces in Rn Antonio Alarcón, Franc Forstnerič, Francisco J. López |
| title_fullStr | New complex analytic methods in the study of non-orientable minimal surfaces in Rn Antonio Alarcón, Franc Forstnerič, Francisco J. López |
| title_full_unstemmed | New complex analytic methods in the study of non-orientable minimal surfaces in Rn Antonio Alarcón, Franc Forstnerič, Francisco J. López |
| title_short | New complex analytic methods in the study of non-orientable minimal surfaces in Rn |
| title_sort | new complex analytic methods in the study of non orientable minimal surfaces in rn |
| topic | Holomorphie (DE-588)4160484-2 gnd Affiner Raum (DE-588)4141574-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Holomorphie Affiner Raum Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032237786&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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