Takeo Ohsawa
Hartogs type extension theorems on some domains in Kähler manifolds
It was recently shown that the boundaries of bounded pseudoconvex domains with $\mathcal C^2$-smooth boundary in Kähler manifolds are connected unless they are Levi flat. The proof is based on a Hartogs type extension theorem. The proof by $L^2$ cohomology vanishing will be sketched and an extension of the method will be discussed.