{"product_id":"9784431562962","title":"Springer Monographs in Mathematics: Development of Oka–Cartan Theory by L² Estimates for the d-bar Operator","description":"\u003ch1\u003eSpringer Monographs in Mathematics: Development of Oka–Cartan Theory by L² Estimates for the d-bar Operator\u003c\/h1\u003e \u003ch2\u003eOhsawa, Takeo\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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 \u003ci\u003eL\u003c\/i\u003e² extension of holomorphic functions.\u003c\/p\u003e\u003cp\u003eIn 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 \u003ci\u003eL\u003c\/i\u003e² 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 \u003ci\u003eL\u003c\/i\u003e² 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 \u003ci\u003eL\u003c\/i\u003e² 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 \u003ci\u003eL\u003c\/i\u003e² method obtained during these 15 years.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2016-08-23\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9784431562962\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-4-431-55747-0\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 196\u003c\/p\u003e ","brand":"Springer Japan","offers":[{"title":"Default Title","offer_id":44521601368204,"sku":"9784431562962","price":80.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9784431562962.jpg?v=1775706114","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9784431562962","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}