Some applications of the Ohsawa-Takegoshi extension theorem
type: Item
instance of: scholarly article
title: Some applications of the Ohsawa-Takegoshi extension theorem
zbMATH Open document ID: 1171.32004
author: Zbigniew Błocki
published in: Expositiones Mathematicae
publication date: 2009-04-23T00:00:00Z
review text: 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.
reviewed by: Harold P. Boas
Mathematics Subject Classification ID: 32D15
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 32W05
zbMATH DE Number: 5546594
zbMATH Keywords: extension of holomorphic functions
zbMATH Keywords: \(L^{2}\)-estimates
zbMATH Keywords: \(\overline{\partial}\)-equation
zbMATH Keywords: Bergman kernel
zbMATH Keywords: plurisubharmonic functions
zbMATH Keywords: Lelong numbers
MaRDI profile type: Publication
full work available at URL: j.exmath.2008.10.004
OpenAlex ID: W2152733082
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DOI: 10.1016/J.EXMATH.2008.10.004
description: scientific article; zbMATH DE number 5546594