Definition:Barrier
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Definition
A complex function $\varphi \in \map \C {\overline \Omega}$ is a barrier for $\Omega$ at $z \in \partial \Omega$ if and only if:
- $\varphi$ is subharmonic
- $\map \varphi z = 0$
- $\varphi < 0$ on $\partial \Omega \setminus \set z$
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Also see
- Definition:Regular Boundary Point: a boundary point $z \in \partial \Omega$ which has a barrier for $\Omega$ at $z \in \partial \Omega$.