Semiglobal results for $\bar{\partial}_{b}$ on weakly convex hypersurfaces in $\mathbb{C}^{n}$

Abstract

Let $M$ be a smoothly bounded weakly convex hypersurface in $\mathbb{C}^{n} (n \geq 4)$, $0 \in M$. Let $q \in \mathbb{N}$, $1 \leq q \le n-2$. We derive a homotopy formula for $\bar{\partial}_{b}$ without shrinking on certain submanifolds of $M$ (no finite type condition is assumed for $M$).