Takeo Ohsawa 
L² Approaches in Several Complex Variables [PDF ebook] 
Towards the Oka–Cartan Theory with Precise Bounds

Support


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.

In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the
L² method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka–Cartan theory is given by this method. The
L² extension theorem with an optimal constant is included, obtained recently by Z. Błocki and separately by Q.-A. Guan and X.-Y. Zhou. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani–Yamaguchi, Berndtsson, Guan–Zhou, and  Berndtsson–Lempert. Most of these results are obtained by the
L² method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the
L² method obtained during the past 15 years.

€117.69
méthodes de payement

Table des matières

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.

Achetez cet ebook et obtenez-en 1 de plus GRATUITEMENT !
Langue Anglais ● Format PDF ● Pages 258 ● ISBN 9784431568520 ● Taille du fichier 3.5 MB ● Maison d’édition Springer Japan ● Lieu Tokyo ● Pays JP ● Publié 2018 ● Édition 2 ● Téléchargeable 24 mois ● Devise EUR ● ID 6734817 ● Protection contre la copie DRM sociale

Plus d’ebooks du même auteur(s) / Éditeur

2 215 Ebooks dans cette catégorie