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A proof of the Ohsawa-Takegoshi theorem with sharp estimates. (English) Zbl 1360.32006

The purpose of this paper is to give a short and concise proof of the Ohsawa-Takegoshi extension theorem with sharp estimates. The authors adapt methods from the proof of Suita’s conjecture [Z. Błocki, Contemp. Math. 644, 1–10 (2015; Zbl 1337.32009)] and use results on positivity of direct image bundles [the author, Ann. Math. (2) 169, No. 2, 531–560 (2009; Zbl 1195.32012)], where, instead of a varying family of domains, they use a varying family of weight functions [Błocki, loc. cit.].

MSC:

32A36 Bergman spaces of functions in several complex variables
32A10 Holomorphic functions of several complex variables