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L² Approaches in Several Complex Variables
- Development of Oka–Cartan Theory by L² Estimates for the d-bar Operator
Af: Takeo Ohsawa
Engelsk
Bogcover for L² Approaches in Several Complex Variables af Takeo Ohsawa, 9784431562962
Specifikationer
Sprog:
Engelsk
Sider:
196
ISBN-13:
9784431562962
Indbinding:
Paperback
ISBN-10:
4431562966
Kategori:
Udg. Dato:
23 aug 2016
Størrelse i cm:
23,5 x 15,5
Forlag:
Serie:
Oplagsdato:
23 aug 2016
Forfatter(e):
Genre:

L² Approaches in Several Complex Variables

- Development of Oka–Cartan Theory by L² Estimates for the d-bar Operator
Af: Takeo Ohsawa
Engelsk
Paperback 2016
Format:
Paperback
Bog beskrivelse
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 L² 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 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. 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 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 these 15 years.
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Specifikationer
Sprog:
Engelsk
Sider:
196
ISBN-13:
9784431562962
Indbinding:
Paperback
ISBN-10:
4431562966
Kategori:
Udg. Dato:
23 aug 2016
Størrelse i cm:
23,5 x 15,5
Forlag:
Serie:
Oplagsdato:
23 aug 2016
Forfatter(e):
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