Ohsawa-Takegoshi type theorem and extension of plurisubharmonic functions

TL;DR

This paper generalizes a theorem of Siu by proving an extension theorem for plurisubharmonic functions across pluripolar sets, utilizing an Ohsawa-Takegoshi type extension theorem in Kähler domains.

Contribution

It introduces a new extension theorem for plurisubharmonic functions across pluripolar sets, based on an Ohsawa-Takegoshi type extension in Kähler domains.

Findings

Extension of plurisubharmonic functions across pluripolar sets

Development of an Ohsawa-Takegoshi type theorem for points in Kähler domains

Generalization of Siu's theorem

Abstract

We prove a Thullen type extension theorem of plurisubharmonic functions across a closed complete pluripolar set, which generalizes a theorem of Siu. Our approach depends on an Ohsawa-Takegoshi type extension theorem for a single point in a bounded complete K\"ahler domain, which is of independent interest.