L(2) Approaches in Several Complex Variables

Development of Oka-Cartan Theory by L(2) Estimates for the d-bar Operator

Autor: Takeo Ohsawa

Język:

Oprawa: Miękka

Wydawca: Springer Verlag, Japan

Dostępność: Dostępna u dostawcy

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The purpose of this monograph is to present the current status of a rapidly developing part of sever...

Informacje o książce

Autor

Takeo Ohsawa

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2016

strony

196

EAN

9784431562962

ISBN

9784431562962

Enbook ID

18341257

Wydawca

Springer Verlag, Japan

Waga

3226

Wymiary

155 x 235 x 12

Pełny opis

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 L ? extension of holomorphic functions. 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 L ? 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 L ? extension theorem with an optimal constant is included, obtained recently by Z. Blocki and by Q.-A. Guan and X.-Y. Zhou separately. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani-Yamaguchi, Berndtsson, and Guan-Zhou. Most of these results are obtained by the L ? 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 L ? method obtained during these 15 years.

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L(2) Approaches in Several Complex Variables

Development of Oka-Cartan Theory by L(2) Estimates for the d-bar Operator

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