Estimates for the $\bar{\partial }$-Neumann problem and nonexistence of Levi-flat hypersurfaces in $C{P}^n$

Jianguo Cao, Mei-Chi Shaw, Lihe Wang

Let $\Omega$ be a pseudoconvex domain with $C^2$-smooth boundary in $\mathbb{C}{P}^n$. We prove that the $\bar{\partial }-Neumannoperator$N$existsfor$(p,q)$-formson$Ω$. Furthermore, th…