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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| Language: | English |
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Tokyo :
Springer Japan : Imprint: Springer,
2015.
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| Edition: | 1st ed. 2015. |
| Series: | Springer Monographs in Mathematics,
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| Online Access: | https://doi.org/10.1007/978-4-431-55747-0 |
Table of Contents:
- 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.