On sharper estimates of Ohsawa–Takegoshi $$L^2$$-extension theorem in higher dimensional case

Abstract

Hosono obtained sharper estimates of the Ohsawa–Takegoshi $$L^2$$ -extension theorem by allowing the constant depending on the weight function for a domain in $${\mathbb {C}}$$ . In this article, we show the higher dimensional case of sharper estimates of the Ohsawa–Takegoshi $$L^2$$ -extension theorem. To prove the higher dimensional case of them, we establish an analogue of Berndtsson–Lempert type $$L^2$$ -extension theorem by using the pluricomplex Green functions with poles along subvarieties. As a special case, we consider the sharper estimates in terms of the Azukawa pseudometric and show that the higher dimensional case of sharper estimate provides the $$L^2$$ -minimum extension for radial case.