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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis L² Approaches in Several Complex Variables
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L² Approaches in Several Complex Variables
Takeo Ohsawa (Gebundene Ausgabe, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
07.10.2015
Sprache
Englisch
EAN
9784431557463
Herausgeber
Springer Tokyo
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Takeo Ohsawa
Seitenanzahl
196
Einbandart
Gebundene Ausgabe
Buch Untertitel
Development of Oka–Cartan Theory by L² Estimates for the d-bar Operator
Schlagwörter
Levi flat hypersurfaces, Vanishing and finiteness theorems, L² extension of holomorphic functions, Multiplier ideals, Bergman kernel
Thema-Inhalt
PBKD - Komplexe Analysis, komplexe Variablen, Funktionentheorie
PBMW - Algebraische Geometrie
PBMP - Differentielle und Riemannsche Geometrie
PBKF - Funktionalanalysis und Abwandlungen
Höhe
235 mm
Breite
15.5 cm
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