Ohsawa-Takegoshi extension theorem for compact K\"ahler manifolds and applications

TL;DR

This paper proves a new extension theorem for sections of the canonical bundle on weakly pseudoconvex K"ahler manifolds with singular metrics, and explores its applications.

Contribution

It introduces a novel extension theorem for canonical bundle sections on weakly pseudoconvex K"ahler manifolds with singular metrics.

Findings

Extension theorem for canonical bundle sections established

Applications to complex geometry demonstrated

Generalization of previous extension results achieved

Abstract

Our main goal in this article is to prove a new extension theorem for sections of the canonical bundle of a weakly pseudoconvex K\"ahler manifold with values in a line bundle endowed with a possibly singular metric. We also give some applications of our result.