Plurisubharmonic Defining Functions in $\mathbb C^2$

Abstract: Let $\Omega={r<0}\subset\mathbb C^2$, with $r$ plurisubharmonic on $b\Omega={r=0}$. Let $\rho$ be another defining function for $\Omega$. A formula for the determinant of the complex Hessian of $\rho$ in terms of $r$ is computed. This formula is used to give necessary and sufficient conditions that make $\rho$ (locally) plurisubharmonic.