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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Alarcón, Antonio
Otros Autores: Forstnerič, Franc, López, Francisco J.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2020.
Colección:Memoirs of the American Mathematical Society Ser.
Temas:
Sprays (Mathematics)
Minimal surfaces.
Holomorphic mappings.
Approximation theory.
Analytic spaces.
Affine differential geometry.
Surfaces minimales.
Applications holomorphes.
Théorie de l'approximation.
Espaces analytiques.
Géométrie différentielle affine.
Affine differential geometry
Analytic spaces
Approximation theory
Holomorphic mappings
Minimal surfaces
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.
Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12} > Holomorphic convexity > Holomorphic and polynomial approximation, Runge pairs, interpolation.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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
  • 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
  • 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

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