Arkiv för Matematik

Volume 60 (2022)

Number 1

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

Pages: 173 – 182

DOI: https://dx.doi.org/10.4310/ARKIV.2022.v60.n1.a7

Authors

Tai Terje Huu Nguyen (Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway)

Xu Wang (Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway)

Abstract

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.

Full Text (PDF format)

Received 21 June 2021

Received revised 20 July 2021

Accepted 16 August 2021

Published 16 May 2022