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

• Κύριος συγγραφέας: Ohsawa, Takeo (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Tokyo : Springer Japan : Imprint: Springer, 2015.
• Έκδοση: 1st ed. 2015.
• Σειρά: Springer Monographs in Mathematics,
• Θέματα: Mathematics.; Algebraic geometry.; Functional analysis.; Functions of complex variables.; Differential geometry.; Several Complex Variables and Analytic Spaces.; Algebraic Geometry.; Differential Geometry.; Functional Analysis.

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...

Πίνακας περιεχομένων:

• 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.