Global Newlander-Nirenberg theorem on domains with finite smooth boundary in complex manifolds

Xianghong Gong, Ziming Shi

Let $M$ be a relatively compact $C^2$ domain in a complex manifold $\mathcal{M}$ of dimension $n$. Assume that $H^1(M,\Theta )=0$ where $\Theta$ is the sheaf of germs of holomorphic tangent…