عنوان

L² approaches in several complex variables :

(Number (ISBN

4431568522

(Number (ISBN

9784431568520

Erroneous ISBN

4431568514

Erroneous ISBN

9784431568513

Title Proper

L² approaches in several complex variables :

General Material Designation

[Book]

Other Title Information

towards the Oka-Cartan theory with precise bounds /

First Statement of Responsibility

Takeo Ohsawa.

Edition Statement

Second edition

Place of Publication, Distribution, etc.

[Tokyo] :

Name of Publisher, Distributor, etc.

Springer Japan KK,

Date of Publication, Distribution, etc.

[2018]

Specific Material Designation and Extent of Item

1 online resource

Series Title

Springer monographs in mathematics

Text of Note

First edition published as "L² approaches in several complex variables: development of Oka-Cartan theory by L² estimates for the ∂̄ operator" in 2015.

Text of Note

Basic notions and classical results -- Analyzing the L² ∂¯-cohomology -- L² Oka-Cartan theory -- Bergman kernels -- L² approaches to holomorphic foliations.

0

Text of Note

"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."--Publisher

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9784431568520

Title

L² approaches in several complex variables.

International Standard Book Number

9784431568513

Analytic spaces.

Functions of several complex variables.

Holomorphic functions.

Analytic spaces.

Functions of several complex variables.

Holomorphic functions.

MAT034000

PBKD

PBKD

Number

Edition

Class number

Book number

Ōsawa, Takeo,1951-

Date of Transaction

20200823200150.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y