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arXiv · 2609.35474

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

Naveen Gupta
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Abstract

Let $D\subseteq \mathbb{C}^n$ be a bounded $\mathbb{C}$-convex domain with $C^1$ 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 $C^{\infty}$ strongly linearly convex domains. This, in particular, answers a question posed by Azinberg \cite{azin} in affirmative for a class of domains $D$.

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Naveen Gupta. 2026-09-28. Strongly linearly convex exhaustion of a class of $\mathbb{C}$-convex domains. https://arxiv.org/abs/2609.35474

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