LEADER 04429nam 22005775 450 001 9910300105103321 005 20200702023206.0 010 $a4-431-56852-2 024 7 $a10.1007/978-4-431-56852-0 035 $a(CKB)4100000007181219 035 $a(MiAaPQ)EBC5607439 035 $a(DE-He213)978-4-431-56852-0 035 $a(PPN)232469946 035 $a(EXLCZ)994100000007181219 100 $a20181128d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLē Approaches in Several Complex Variables $eTowards the Oka?Cartan Theory with Precise Bounds /$fby Takeo Ohsawa 205 $a2nd ed. 2018. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2018. 215 $a1 online resource (267 pages) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 311 $a4-431-56851-4 327 $aPart I Holomorphic Functions and Complex Spaces -- Convexity Notions -- Complex Manifolds -- Classical Questions of Several Complex Variables -- Part II The Method of Lē Estimates -- Basics of Hilbert Space Theory -- Harmonic Forms -- Vanishing Theorems -- Finiteness Theorems -- Notes on Complete Kahler Domains (= CKDs) -- Part III Lē 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 Lē Approaches to Holomorphic Foliations -- Holomorphic Foliation and Stable Sets -- Lē Method Applied to Levi Flat Hypersurfaces -- LFHs in Tori and Hopf Surfaces. 330 $aThis monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Special emphasis is put on the new precise results on the Lē extension of holomorphic functions in the past 5 years. In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the Lē method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka?Cartan theory is given by this method. The Lē extension theorem with an optimal constant is included, obtained recently by Z. B?ocki and separately by Q.-A. Guan and X.-Y. Zhou. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani?Yamaguchi, Berndtsson, Guan?Zhou, and Berndtsson?Lempert. Most of these results are obtained by the Lē method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the Lē method obtained during the past 15 years. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aFunctions of complex variables 606 $aAlgebraic geometry 606 $aDifferential geometry 606 $aFunctional analysis 606 $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aFunctions of complex variables. 615 0$aAlgebraic geometry. 615 0$aDifferential geometry. 615 0$aFunctional analysis. 615 14$aSeveral Complex Variables and Analytic Spaces. 615 24$aAlgebraic Geometry. 615 24$aDifferential Geometry. 615 24$aFunctional Analysis. 676 $a515.94 700 $aOhsawa$b Takeo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755713 906 $aBOOK 912 $a9910300105103321 996 $aLē Approaches in Several Complex Variables$91910225 997 $aUNINA