Diederich–Pinchuk extension conjecture for proper holomorphic mappings

Let $D,D'\subset\mathbb{C}^n$, with $n\geq 2$, be bounded domains whose boundaries are real analytic and geometrically smooth, and let $h:D\to D'$ be a proper holomorphic mapping. Diederich–Pinchuk's extension conjecture. The map $h$ extends holomorphically to an open neighborhood of $\overline{D}$ in $\mathbb{C}^n$. The conjecture was solved without a pseudoconvexity assumption when $n=2$, but is open for $n\geq 3$ to the author's knowledge.