L² Approaches in Several Complex Variables Development of Oka-Cartan Theory by L² Estimates for the d-bar Operator /

The purpose of this monograph is to present the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Highlighted are the new precise results on the L² extension of holomorphic fu...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ohsawa, Takeo (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Tokyo : Springer Japan : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Colección:Springer Monographs in Mathematics,
Temas:
Functions of complex variables.
Algebraic geometry.
Geometry, Differential.
Functional analysis.
Several Complex Variables and Analytic Spaces.
Algebraic Geometry.
Differential Geometry.
Functional Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Part I Holomorphic Functions and Complex Spaces
  • Convexity Notions
  • Complex Manifolds
  • Classical Questions of Several Complex Variables
  • Part II The Method of L² Estimates
  • Basics of Hilb ert Space Theory
  • Harmonic Forms
  • Vanishing Theorems
  • Finiteness Theorems
  • Notes on Complete Kahler Domains (= CKDs)
  • Part III L² Variant of Oka-Cartan Theory
  • Extension Theorems
  • Division Theorems
  • Multiplier Ideals
  • Part IV Bergman Kernels
  • The Bergman Kernel and Metric
  • Bergman Spaces and Associated Kernels
  • Sequences of Bergman Kernels
  • Parameter Dependence
  • Part V L² Approaches to Holomorphic Foliations
  • Holomorphic Foliation and Stable Sets
  • L² Method Applied to Levi Flat Hypersurfaces
  • LFHs in Tori and Hopf Surfaces.

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