A note on plurisubharmonic defining functions in $${\mathbb{C}^{n}}$$

Abstract

Let \({\Omega\subset\subset\mathbb{C}^{n}}\) , n ≥ 3, be a smoothly bounded domain. Suppose that Ω admits a smooth defining function which is plurisubharmonic on the boundary of Ω. Then a Diederich–Fornaess exponent can be chosen arbitrarily close to 1, and the closure of Ω admits a Stein neighborhood basis.