L² approaches in several complex variables development of OkaCartan Theory by L² estimates for the [delta bar] operator /
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 fu...
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Format:  Electronic eBook 
Language:  English 
Imprint:  Tokyo ; New York : Springer, [2015] 
Series:  Springer monographs in mathematics.

Subjects:  
Online Access:  Available in Springer Mathematics and Statistics eBooks 2015 English/International. 
LEADER  02911cam a22003253i 4500  

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003  EBZ  
006  m o d   
007  crunu  
008  150630t20152015ja job 001 0 eng c  
020  z 9784431557463  
020  a 9784431557470 (online)  
035  a (OCoLC)ocn921827580  
035  a (EBZ)ebs7160161e  
040  a CDX b eng d EBZ  
042  a pcc  
050  0  0  a QA331.7 b .O82 2015 
100  1  a Ōsawa, Takeo, d 1951 e author.  
245  1  0  a L² approaches in several complex variables h [electronic resource] : b development of OkaCartan Theory by L² estimates for the [delta bar] operator / c Takeo Ohsawa. 
264  1  a Tokyo ; a New York : b Springer, c [2015]  
264  4  c ©2015  
490  1  a Springer monographs in mathematics  
504  a Includes bibliographical references (pages 177191) and index.  
520  a 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 deltabar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the OkaCartan theory is given by this method. The L² extension theorem with an optimal constant is included, obtained recently by Z. Błocki 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 MaitaniYamaguchi, Berndtsson, and GuanZhou. 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  c Source other than the Library of Congress.  
650  0  a Functions of several complex variables.  
650  7  a Functions of several complex variables. 2 fast 0 (OCoLC)fst00936123  
773  0  t Springer Mathematics and Statistics eBooks 2015 English/International d Springer Nature  
776  1  t L² approaches in several complex variables w (OCoLC)ocn921827580 w (DLC)2015945263  
830  0  a Springer monographs in mathematics.  
856  4  0  3 Full text available z Available in Springer Mathematics and Statistics eBooks 2015 English/International. u https://ezproxy.wellesley.edu/login?url=https://link.springer.com/10.1007/9784431557470 