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New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Mathbb{R}^{n}
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 \mathbb{R}^n for any n\ge 3. These methods, which the authors develop essentially from the first principles, enable them to prove that the space...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2020.
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| Colección: | Memoirs of the American Mathematical Society Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Mu 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_on1223095038 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 201121s2020 riu o ||| 0 eng d | ||
| 040 | |a EBLCP |b eng |c EBLCP |d LOA |d OCLCO |d OCLCF |d OCLCO |d OCLCQ |d OCLCO | ||
| 020 | |a 9781470458126 | ||
| 020 | |a 1470458128 | ||
| 029 | 1 | |a AU@ |b 000069468711 | |
| 035 | |a (OCoLC)1223095038 | ||
| 050 | 4 | |a QA644 |b .A437 2020 | |
| 082 | 0 | 4 | |a 516.3/62 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Alarcón, Antonio. | |
| 245 | 1 | 0 | |a New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Mathbb{R}^{n} |h [electronic resource]. |
| 260 | |a Providence : |b American Mathematical Society, |c 2020. | ||
| 300 | |a 1 online resource (90 p.). | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v v.264 | |
| 500 | |a Description based upon print version of record. | ||
| 505 | 0 | |a Cover -- Title page -- Chapter 1. Introduction -- 1.1. A summary of the main results -- 1.2. Basic notions of minimal surface theory -- 1.3. Approximation and general position theorems -- 1.4. Complete non-orientable minimal surfaces with Jordan boundaries -- 1.5. Proper non-orientable minimal surfaces in domains in \Rⁿ -- Chapter 2. Preliminaries -- 2.1. Conformal structures on surfaces -- 2.2. \Igot-invariant functions and 1-forms. Spaces of functions and maps -- 2.3. Homology basis and period map -- 2.4. Conformal minimal immersions of non-orientable surfaces -- 2.5. Notation | |
| 505 | 8 | |a Chapter 3. Gluing \Igot-invariant sprays and applications -- 3.1. \Igot-invariant sprays -- 3.2. Gluing \Igot-invariant sprays on \Igot-invariant Cartan pairs -- 3.3. \Igot-invariant period dominating sprays -- 3.4. Banach manifold structure of the space \CMI_{\Igot}ⁿ(\Ncal) -- 3.5. Basic approximation results -- 3.6. The Riemann-Hilbert method for non-orientable minimal surfaces -- Chapter 4. Approximation theorems for non-orientable minimal surfaces -- 4.1. A Mergelyan approximation theorem -- 4.2. A Mergelyan theorem with fixed components | |
| 505 | 8 | |a Chapter 5. A general position theorem for non-orientable minimal surfaces -- Chapter 6. Applications -- 6.1. Proper non-orientable minimal surfaces in \Rⁿ -- 6.2. Complete non-orientable minimal surfaces with fixed components -- 6.3. Complete non-orientable minimal surfaces with Jordan boundaries -- 6.4. Proper non-orientable minimal surfaces in -convex domains -- Bibliography -- Back Cover | |
| 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 \mathbb{R}^n for any n\ge 3. These methods, which the authors develop essentially from the first principles, enable them to prove that the space of conformal minimal immersions of a given bordered non-orientable surface to \mathbb{R}^n is a real analytic Banach manifold, obtain approximation results of Runge-Mergelyan type for conformal minimal immersions from non-orientable surfaces, and show general position theorems for non-orientable co. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Sprays (Mathematics) | |
| 650 | 0 | |a Minimal surfaces. | |
| 650 | 0 | |a Holomorphic mappings. | |
| 650 | 0 | |a Approximation theory. | |
| 650 | 0 | |a Analytic spaces. | |
| 650 | 0 | |a Affine differential geometry. | |
| 650 | 6 | |a Surfaces minimales. | |
| 650 | 6 | |a Applications holomorphes. | |
| 650 | 6 | |a Théorie de l'approximation. | |
| 650 | 6 | |a Espaces analytiques. | |
| 650 | 6 | |a Géométrie différentielle affine. | |
| 650 | 7 | |a Affine differential geometry |2 fast | |
| 650 | 7 | |a Analytic spaces |2 fast | |
| 650 | 7 | |a Approximation theory |2 fast | |
| 650 | 7 | |a Holomorphic mappings |2 fast | |
| 650 | 7 | |a Minimal surfaces |2 fast | |
| 650 | 7 | |a Sprays (Mathematics) |2 fast | |
| 650 | 7 | |a Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12} -- Local analytic geometry [See also 13-XX and 14-XX] -- Analytic subsets of affine space. |2 msc | |
| 650 | 7 | |a Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12} -- Holomorphic convexity -- Holomorphic and polynomial approximation, Runge pairs, interpolation. |2 msc | |
| 700 | 1 | |a Forstnerič, Franc. | |
| 700 | 1 | |a López, Francisco J. | |
| 776 | 0 | 8 | |i Print version: |a Alarcón, Antonio |t New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Mathbb{R}^{n} |d Providence : American Mathematical Society,c2020 |z 9781470441616 |
| 830 | 0 | |a Memoirs of the American Mathematical Society Ser. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6195962 |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6195962 | ||
| 994 | |a 92 |b IZTAP | ||