L² Approaches in Several Complex Variables
Towards the Oka¿Cartan Theory with Precise Bounds
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ISBN-13:
9784431568513
Veröffentl:
2018
Einband:
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Erscheinungsdatum:
10.12.2018
Seiten:
272
Autor:
Takeo Ohsawa
Gewicht:
576 g
Format:
241x160x21 mm
Serie:
Springer Monographs in Mathematics
Sprache:
Englisch
Beschreibung:
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 in the past 5 years.
Presents quite recent research works, all of very high standard, in the field of several complex variables
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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