L2 Approaches in Several Complex Variables Towards the Oka-Cartan Theory with Precise Bounds /

This monograph presents 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. Special emphasis is put on the new precise results on the L2 extension of holomorphic functions i...

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Hlavný autor: Ohsawa, Takeo (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:English
Vydavateľské údaje: Tokyo : Springer Japan , 2018.
Vydanie:2nd ed. 2018.
Edícia:Springer Monographs in Mathematics,
Predmet:
Functions of complex variables.
Algebraic geometry.
Differential geometry.
Functional analysis.
ISBN:9784431568520
ISSN:1439-7382
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Obsah:
  • 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 Hilbert 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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