LEADER 04503nam 22007095 450 001 9910300252203321 005 20251113155222.0 010 $a4-431-55747-4 024 7 $a10.1007/978-4-431-55747-0 035 $a(CKB)3710000000484673 035 $a(EBL)4179006 035 $a(SSID)ssj0001585248 035 $a(PQKBManifestationID)16265205 035 $a(PQKBTitleCode)TC0001585248 035 $a(PQKBWorkID)14865621 035 $a(PQKB)11515220 035 $a(DE-He213)978-4-431-55747-0 035 $a(MiAaPQ)EBC4179006 035 $a(PPN)189366354 035 $a(EXLCZ)993710000000484673 100 $a20150928d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLČ Approaches in Several Complex Variables $eDevelopment of Oka?Cartan Theory by LČ Estimates for the d-bar Operator /$fby Takeo Ohsawa 205 $a1st ed. 2015. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2015. 215 $a1 online resource (202 p.) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 300 $aDescription based upon print version of record. 311 08$a4-431-55746-6 320 $aIncludes bibliographical references and index. 327 $aPart I Holomorphic Functions and Complex Spaces -- Convexity Notions -- Complex Manifolds -- Classical Questions of Several Complex Variables -- Part II The Method of LČ Estimates -- Basics of Hilb ert Space Theory -- Harmonic Forms -- Vanishing Theorems -- Finiteness Theorems -- Notes on Complete Kahler Domains (= CKDs) -- Part III LČ 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 LČ Approaches to Holomorphic Foliations -- Holomorphic Foliation and Stable Sets -- LČ Method Applied to Levi Flat Hypersurfaces -- LFHs in Tori and Hopf Surfaces. 330 $aThe purpose of this monograph is to present the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Highlighted are the new precise results on the LČ extension of holomorphic functions. In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the LČ method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka?Cartan theory is given by this method. The LČ extension theorem with an optimal constant is included, obtained recently by Z. B?ocki and by Q.-A. Guan and X.-Y. Zhou separately. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani?Yamaguchi, Berndtsson, and Guan?Zhou. Most of these results are obtained by the LČ method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the LČ method obtained during these 15 years. 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aFunctions of complex variables 606 $aAlgebraic geometry 606 $aGeometry, Differential 606 $aFunctional analysis 606 $aSeveral Complex Variables and Analytic Spaces 606 $aAlgebraic Geometry 606 $aDifferential Geometry 606 $aFunctional Analysis 615 0$aFunctions of complex variables. 615 0$aAlgebraic geometry. 615 0$aGeometry, Differential. 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$0755713 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300252203321 996 $aLČ Approaches in Several Complex Variables$91910225 997 $aUNINA