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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
L² Approaches in Several Complex Variables: Towards the Oka-Cartan Theory with Precise Bounds

L² Approaches in Several Complex Variables: Towards the Oka-Cartan Theory with Precise Bounds

Ohsawa, Takeo

Hardcover

Series: Springer Monographs in Mathematics

General MathematicsGeometry

ISBN10: 4431568514
ISBN13: 9784431568513
Publisher: Springer Nature
Published: Dec 10 2018
Pages: 258
Weight: 1.23
Height: 0.63 Width: 6.14 Depth: 9.21
Language: English
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 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 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 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 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 method obtained during the past 15 years.

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