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

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 $X$.Comment: 4 pages; to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5

On the Ohsawa-Takegoshi L2L^2 extension theorem and removable singularities of plurisubharmonic functions

The celebrated Ohsawa-Takegoshi extension theorem for $L^2$ holomorphic functions on bounded pseudoconvex domains in $\mathbb C^n$ is an important and powerful tool in several complex variables and complex geometry. Ohsawa conjectured in 1995 that the same theorem holds for more general bounded complete K\"ahler domains in $\mathbb C^n$. Recently, Chen-Wu-Wang confirmed this conjecture in a special case. In this paper we extend their result to the case of holomorphic sections of twisted canonical bundles over relatively compact complete K\"{a}hler domains in Stein manifolds. As an application we prove a Hartogs type extension theorem for plurisubharmonic functions across a compact complete pluripolar set, which is complementary to a classical theorem of Shiffman and can be thought of as an analogue of the Skoda-El Mir extension theorem for plurisubharmonic functions.Comment: 18 page

Complete pluripolar sets and removable singularities of plurisubharmonic functions

Inspired by Chen-Wu-Wang (Math. Ann. 362: 305--319, 2015), we prove a Hartogs type extension theorem for plurisubharmonic functions across a compact complete pluripolar set, which is complementary to a classical theorem of Shiffman.Comment: 5 page