L[2] approaches in several complex variables : towards the Oka-Cartan Theory with precise bounds

書誌事項

L[2] approaches in several complex variables : towards the Oka-Cartan Theory with precise bounds

Takeo Ohsawa

(Springer monographs in mathematics)

Springer, c2018

2nd ed

タイトル別名

L2 approaches in several complex variables : towards the Oka-Cartan Theory with precise bounds

大学図書館所蔵 件 / 16

この図書・雑誌をさがす

注記

[2] is subscript

Includes bibliographical references (p. 239-253) and index

内容説明・目次

内容説明

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 L(2) 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 L(2) 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(2) extension theorem with an optimal constant is included, obtained recently by Z. Blocki 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 L(2) 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(2) method obtained during the past 15 years.

目次

L(2)

「Nielsen BookData」 より

関連文献: 1件中  1-1を表示

詳細情報

ページトップへ