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.
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Acknowledgements
The author would like to thank Prof. Ryoichi Kobayashi and Dr. Genki Hosono for valuable comments.
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The authors state that there is no conflict of interest. The article has associated date in the Nagoya Repository (https://nagoya.repo.nii.ac.jp).
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Kikuchi, S. On sharper estimates of Ohsawa–Takegoshi \(L^2\)-extension theorem in higher dimensional case. manuscripta math. 170, 453–469 (2023). https://doi.org/10.1007/s00229-021-01366-8
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DOI: https://doi.org/10.1007/s00229-021-01366-8