# The generalization of Hartogs' Theorem

I know a version of Hartogs' Theorem in the book An introduction to complex analysis(p 30) by Hormander, namely Hartogs' Theorem when K compact with complement being simply connected

I also have learned another version in Hodge Theory and Complex Algebraic Geometry I (p34) by Voisin. Hartogs' Theorem when $K=\{z_1=z_2=0\}$

My question: are there any generalizations of Hartogs' Theorem, with respect to $K$ (i.e. we only change the condition of $K$, confining the stage in $\mathbb{C}^{n}$ )?

Any clue is welcome. Many Thanks!