English

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

Complex Variables 2021-05-04 v1 Algebraic Geometry

Abstract

We utilize the Legendre-Fenchel transform and weak geodesics for plurisubharmonic functions to construct a weight function that can be used in the Berndtsson-Lempert method, to give an Ohsawa-Takegoshi extension type of result. Theorem 4.1 and Theorem 0.1 in \cite{OT2017} (Theorem \ref{Theorem A} and \ref{Theorem B} below) follow as two special cases of this result, thus answering affirmatively a question posed by Ohsawa in remark 4.1 in \cite{OT2017}, on the Berndtsson-Lempert method.

Keywords

Cite

@article{arxiv.2105.00947,
  title  = {On a remark by Ohsawa related to the Berndtsson-Lempert method for $L^2$-holomorphic extension},
  author = {Tai Terje Huu Nguyen and Xu Wang},
  journal= {arXiv preprint arXiv:2105.00947},
  year   = {2021}
}