Oberseminar: Pascal Thomas (G.15.25)
We show that for bounded domains in $\mathbb{C}^n$ with $\mathcal{C}^{1,1}$-smooth boundary, if there is a closed set $F$ of $2n-1$-Lebesgue measure $0$ such that $\partial \Omega \setminus F$ is $\mathcal{C}^{2}$-smooth and locally pseudoconvex at every point, then $\Omega$ is globally pseudoconvex. Unlike the globally $\mathcal{C}^{2}$-smooth case, the condition "$F$ of (relative) empty interior" is not enough to obtain such a result.
