Ohsawa-Takegoshi \(L^2\) extension theorem: revisited
type: Item
instance of: scholarly article
zbMATH Open document ID: 1250.32008
publication date: 2012-07-21T00:00:00Z
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32Q15
Mathematics Subject Classification ID: 32W50
zbMATH DE Number: 6059324
zbMATH Keywords: plurisubharmonic weights
zbMATH Keywords: Bochner-Kodaira-Nakano formula
zbMATH Keywords: holomorphic vector bundles
author: Xiangyu Zhou
author: Langfeng Zhu
MaRDI profile type: Publication
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title: Ohsawa-Takegoshi \(L^2\) extension theorem: revisited
review text: The article surveys different approaches to the proof of the famous extension theorem of T. Ohsawa and K. Takegoshi for weighted square-integrable holomorphic functions and its generalizations. The authors first go into the proof of the original version that was stated in the context of Stein manifolds and holomorphic forms and which is based on computations involving complete Kähler metrics. Then they treat a proof due to Siu that works without complete Kähler metrics and uses a ``twisted Morrey-Kohn-Hörmander formula'' instead. In the next section the generalizations due to Manivel and Demailly are discussed, where holomorphic extension results for holomorphic sections in certain hermitian vector bundles are established.NEWLINENEWLINEAfter this the approach of Berndtsson is treated, where the key lemma is a solution theorem for \(\bar \partial \) at the level of currents.NEWLINENEWLINEFinally, the authors sketch Ohsawa's version that works with negligible weights. The authors conclude their survey article with a section containing their own contributions to this theme (see [\textit{Q. Guan} and the authors, C. R., Math., Acad. Sci. Paris 349, No. 13--14, 797--800 (2011; Zbl 1227.32014)]).NEWLINENEWLINEFor the entire collection see [Zbl 1235.00045].
reviewed by: Gregor Herbort
description: scientific article; zbMATH DE number 6059324