Bott-Chern cohomology and the Hartogs extension theorem for pluriharmonic functions

TL;DR

This paper establishes a vanishing result for Bott-Chern cohomology on certain complex manifolds, leading to a Hartogs extension theorem for pluriharmonic functions, thus advancing understanding of complex analysis and cohomology.

Contribution

It proves a new vanishing theorem for Bott-Chern cohomology on cohomologically $(n-1)$-complete manifolds, enabling Hartogs extension for pluriharmonic functions.

Findings

Vanishing of Bott-Chern cohomology group of type (1,1) with compact support.

Extension of pluriharmonic functions across certain complex manifolds.

Application of Ehrenpreis technique to cohomology results.

Abstract

Let $X$ be a cohomologically $(n-1)$-complete complex manifold of dimension $n\geq 2$. We prove a vanishing result for the Bott-Chern cohomology group of type $(1, 1)$ with compact support in $X$, which combined with the well-known technique of Ehrenpreis implies a Hartogs type extension theorem for pluriharmonic functions on $X$.