A note on plurisubharmonic defining functions in $$\mathbb{C}^2$$

Abstract

Let Ω ⊂⊂ $$\mathbb{C}^2$$ be a smoothly bounded domain. Suppose that Ω admits a smooth defining function which is plurisubharmonic on the boundary of Ω. Then the Diederich-Fornaess exponent can be chosen arbitrarily close to 1, and the closure of Ω admits a Stein neighborhood basis.