Definition:Barrier

Definition
A complex function $\varphi \in \map \C {\overline \Omega}$ is a barrier for $\Omega$ at $z \in \partial \Omega$ :
 * $\varphi$ is subharmonic
 * $\map \varphi z = 0$
 * $\varphi < 0$ on $\partial \Omega \setminus \set z$

Also see

 * Definition:Regular Boundary Point: a boundary point $z \in \partial \Omega$ which has a barrier for $\Omega$ at $z \in \partial \Omega$.