关于Ohsawa关于$L^2$-全纯扩张的Berndtsson–Lempert方法的一点注记

IF 0.8 4区数学 Q2 MATHEMATICS

Arkiv for Matematik Pub Date : 2021-05-03 DOI:10.4310/arkiv.2022.v60.n1.a7

T. Nguyen, Xu Wang

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引用次数: 1

摘要

在[15，备注4.1]中，Ohsawa询问是否可以使用Berndtsson Lempert方法证明[15]中的定理4.1和定理0.1。我们将在本文中正式回答大泽的问题。我们的方法还建议将勒让德-芬切尔理论和弱psh测地线引入到Berndtsson-Lempert方法中。

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On a remark by Ohsawa related to the Berndtsson–Lempert method for $L^2$-holomorphic extension

. In [15, Remark 4.1], Ohsawa asked whether it is possible to prove Theorem 4.1 and Theorem 0.1 in [15] using the Berndtsson-Lempert method. We shall answer Ohsawa’s question aﬃrmatively in this paper. Our approach also suggests to introduce the Legendre-Fenchel theory and weak psh-geodesics into the Berndtsson-Lempert method.

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