Strongly linearly convex exhaustion of a class of $\mathbb{C}$-convex domains

Abstract: Let $D\subseteq \mathbb{C}<sup>n$ be a bounded $\mathbb{C}$-convex domain with $C<sup>1$ boundary whose outward unit normal admits a modulus of continuity $ω$ satisfying $\lim_{t\to 0^{+}\dfrac{ω(t)}{\sqrt} t}$. We prove that $D$ admits an increasing exhaustion by bounded $C<sup>{\infty}$ strongly linearly convex domains. This, in particular, answers a question posed by Azinberg \cite{azin} in affirmative for a class of domains $D$.