Some applications of the Ohsawa-Takegoshi extension theorem (Q1012901)

This expository article first sketches a proof due to Bo Berndtsson of the original version of the Ohsawa--Takegoshi extension theorem for \(L^{2}\) holomorphic functions on affine slices of bounded pseudoconvex domains in \(\mathbb{C}^n\) [\textit{T. Ohsawa} and \textit{K. Takegoshi}, Math. Z. 195, 197--204 (1987; Zbl 0625.32011)]. Then the author discusses three applications: lower bounds on the growth of the Bergman kernel function on the diagonal at the boundary of a pseudoconvex domain; the Suita conjecture; and J.-P. Demailly's approximation of plurisubharmonic functions.