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L² Approaches in Several Complex Variables = Towards the Oka–Cartan Theory with Precise Bounds /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	L² Approaches in Several Complex Variables/ by Takeo Ohsawa.
其他題名:	Towards the Oka–Cartan Theory with Precise Bounds /
作者:	Ohsawa, Takeo.
面頁冊數:	XI, 258 p. 5 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Functions of complex variables. -
電子資源:	https://doi.org/10.1007/978-4-431-56852-0
ISBN:	9784431568520

L² Approaches in Several Complex Variables = Towards the Oka–Cartan Theory with Precise Bounds /
Ohsawa, Takeo.

L² Approaches in Several Complex VariablesTowards the Oka–Cartan Theory with Precise Bounds /[electronic resource] :by Takeo Ohsawa. - 2nd ed. 2018. - XI, 258 p. 5 illus.online resource. - Springer Monographs in Mathematics,1439-7382. - Springer Monographs in Mathematics,.

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.

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.

ISBN: 9784431568520

Standard No.: 10.1007/978-4-431-56852-0doiSubjects--Topical Terms:

528649
Functions of complex variables.

LC Class. No.: QA331.7

Dewey Class. No.: 515.94

L² Approaches in Several Complex Variables = Towards the Oka–Cartan Theory with Precise Bounds /
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