Property ($P$) and Stein neighborhood bases on $C^1$ domains

Abstract

Let $Ω$ be a bounded domain in $ℂ^n$ satisfying Catlin’s Property ($P$). Sibony has shown that $\overline{\Omega}$ possesses a Stein neighborhood basis when the boundary is of class $C^3$. In this paper, we use an alternative characterization of such domains to show that Sibony’s result holds when the boundary is of class $C^1$.