Oberseminar: Takeo Ohsawa (G.15.20)
Boundary of complex manifolds has rich structures. They are related to the structure of the interior by Hartogs-type extension theorems. Certain irregular boundary points can be removed by proper modification. In such a situation, arising in a counterexample of Fornaess to Oka's conjecture on ramified Riemann domains over $\mathbb{C}^2$, one can apply the $L^2$-method to produce holomorphic functions separating the points. This can be regarded as an extension from boundary points. Existence of a complete Kähler metric is crucial for the application of the $L^2$-method here.
