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Springer Monographs in Mathematics

L² Approaches in Several Complex Variables

Development of Oka–Cartan Theory by L² Estimates for the d-bar Operator

Authors: Ohsawa, Takeo

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  • Presents quite recent research works, all of very high standard, in the field of several complex variables
  • Selects only extremely important materials from the conventional basic theory of complex analysis and manifold theory
  • Requires no more than a one-semester introductory course in complex analysis as a prerequisite for understanding
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eBook 59,49 €
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  • ISBN 978-4-431-55747-0
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Softcover 69,99 €
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  • ISBN 978-4-431-56296-2
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  • Usually dispatched within 3 to 5 business days.
About this book

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. 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 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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook 59,49 €
price for India (gross)
  • ISBN 978-4-431-55747-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 69,99 €
price for India (gross)
  • ISBN 978-4-431-56296-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
L² Approaches in Several Complex Variables
Book Subtitle
Development of Oka–Cartan Theory by L² Estimates for the d-bar Operator
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2015
Publisher
Springer Japan
Copyright Holder
Springer Japan
eBook ISBN
978-4-431-55747-0
DOI
10.1007/978-4-431-55747-0
Softcover ISBN
978-4-431-56296-2
Series ISSN
1439-7382
Edition Number
1
Number of Pages
IX, 196
Topics