國立虎尾科技大學 |

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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	L² Approaches in Several Complex Variables/ by Takeo Ohsawa.
Reminder of title:	Towards the Oka–Cartan Theory with Precise Bounds /
Author:	Ohsawa, Takeo.
Description:	XI, 258 p. 5 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functions of complex variables. -
Online resource:	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 /
LDR:03583nam a22003975i 4500 001 989815
003 DE-He213
005 20200702023206.0
007 cr nn 008mamaa
008 201225s2018 ja | s |||| 0|eng d
020 $a 9784431568520 $9 978-4-431-56852-0
024 7 $a 10.1007/978-4-431-56852-0 $2 doi
035 $a 978-4-431-56852-0
050 4 $a QA331.7
072 7 $a PBKD $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKD $2 thema
082 0 4 $a 515.94 $2 23
100 1 $a Ohsawa, Takeo. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1211349
245 1 0 $a L² Approaches in Several Complex Variables $h [electronic resource] : $b Towards the Oka–Cartan Theory with Precise Bounds / $c by Takeo Ohsawa.
250 $a 2nd ed. 2018.
264 1 $a Tokyo : $b Springer Japan : $b Imprint: Springer, $c 2018.
300 $a XI, 258 p. 5 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer Monographs in Mathematics, $x 1439-7382
505 0 $a 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.
520 $a 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.
650 0 $a Functions of complex variables. $3 528649
650 0 $a Algebraic geometry. $3 1255324
650 0 $a Differential geometry. $3 882213
650 0 $a Functional analysis. $3 527706
650 1 4 $a Several Complex Variables and Analytic Spaces. $3 672032
650 2 4 $a Algebraic Geometry. $3 670184
650 2 4 $a Differential Geometry. $3 671118
650 2 4 $a Functional Analysis. $3 672166
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9784431568513
776 0 8 $i Printed edition: $z 9784431568537
830 0 $a Springer Monographs in Mathematics, $x 1439-7382 $3 1254272
856 4 0 $u https://doi.org/10.1007/978-4-431-56852-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)