Ohsawa-Takegoshi \(L^2\) extension theorem: revisited
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].
scientific article; zbMATH DE number 6059324
scientific article