| 书目名称 | L² Approaches in Several Complex Variables | | 副标题 | Towards the Oka–Cart | | 编辑 | Takeo Ohsawa | | 视频video | | | 概述 | Presents quite recent research works, all of very high standard, in the field of several complex variables.Selects only extremely important materials from the conventional basic theory of complex anal | | 丛书名称 | Springer Monographs in Mathematics | | 图书封面 |  | | 描述 | This 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 .L². 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 .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 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 .L². method. In the last chapter, rat | | 出版日期 | Book 2018Latest edition | | 关键词 | Bergman kernel; Levi flat hypersurfaces; L² extension of holomorphic functions; Multiplier ideals; Vanis | | 版次 | 2 | | doi | https://doi.org/10.1007/978-4-431-56852-0 | | isbn_ebook | 978-4-431-56852-0Series ISSN 1439-7382 Series E-ISSN 2196-9922 | | issn_series | 1439-7382 | | copyright | Springer Japan KK, part of Springer Nature 2018 |
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发表于 2025-3-21 20:08:10
