{"product_id":"9789811912382","title":"SpringerBriefs in Mathematics","description":"\u003ch1\u003eSpringerBriefs in Mathematics\u003c\/h1\u003e \u003ch2\u003eOhsawa, Takeo; Pawlaschyk, Thomas\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe focus of this book is on the further development of the classical achievements in analysis of several complex variables, the analytic continuation and the analytic structure of sets, to settings in which the  \u003ci\u003eq-\u003c\/i\u003epseudoconvexity in the sense of Rothstein and the \u003ci\u003eq-\u003c\/i\u003econvexity in the sense of Grauert play a crucial role. After giving a brief survey of notions of generalized convexity and their most important results, the authors present recent statements on analytic continuation related to them. \u003c\/p\u003e\n\nRothstein (1955) first introduced \u003ci\u003eq-\u003c\/i\u003epseudoconvexity using generalized Hartogs figures. Słodkowski (1986) defined \u003ci\u003eq-\u003c\/i\u003epseudoconvex sets by means of the existence of exhaustion functions which are \u003ci\u003eq-\u003c\/i\u003eplurisubharmonic in the sense of Hunt and Murray (1978). Examples of \u003ci\u003eq-\u003c\/i\u003epseudoconvex sets appear as complements of  analytic sets. Here, the relation of the analytic structure of graphs of continuous surfaces whose complements are \u003ci\u003eq-\u003c\/i\u003epseudoconvex is investigated. As an outcome, the authors generalize results by Hartogs (1909), Shcherbina (1993), and Chirka (2001) on the existence of foliations of pseudoconcave continuous real hypersurfaces by smooth complex ones. \u003cp\u003e\u003c\/p\u003e\n\n\u003cp\u003eA similar generalization is obtained by a completely different approach using L²-methods in the setting of \u003ci\u003eq-\u003c\/i\u003econvex spaces. The notion of \u003ci\u003eq-\u003c\/i\u003econvexity was developed by Rothstein (1955) and Grauert (1959) and extended to \u003ci\u003eq-\u003c\/i\u003econvex spaces by Andreotti and Grauert (1962). Andreotti–Grauert's finiteness theorem was applied by Andreotti and Norguet (1966–1971) to extend Grauert's solution of the Levi problem to \u003ci\u003eq-\u003c\/i\u003econvex spaces. A consequence is that the sets of (\u003ci\u003eq-\u003c\/i\u003e1)-cycles of \u003ci\u003eq-\u003c\/i\u003econvex domains with smooth boundaries in projective algebraic manifolds, which are equipped with complex structures as open subsets of Chow varieties, are in fact holomorphically convex. Complements of analytic curves are studied,and the relation of \u003ci\u003eq-\u003c\/i\u003econvexity and cycle spaces is explained. Finally, results for \u003ci\u003eq-\u003c\/i\u003econvex domains in projective spaces are shown and the \u003ci\u003eq-\u003c\/i\u003econvexity in analytic families is investigated.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2022-06-03\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9789811912382\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-981-19-1239-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 58\u003c\/p\u003e ","brand":"Springer Nature Singapore","offers":[{"title":"Default Title","offer_id":44541760012428,"sku":"9789811912382","price":53.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789811912382.jpg?v=1775785941","url":"https:\/\/lateknightbooks.com\/products\/9789811912382","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}