Diederich--Fornæss index and global regularity in the $\overline{\partial }$--Neumann problem: domains with comparable Levi eigenvalues

Bingyuan Liu, Emil J. Straube

Let $\hat{I}\text{c◯}$ be a smooth bounded pseudoconvex domain in ${\mathbb{C}}^n$. Let $1\le q_0\le (n-1)$. We show that if $q_0$--sums of eigenvalues of the Levi form are comparable, the…