# is the converse true: in a simply connected domain every harmonic function has its conjugate

The question is.

Is the converse true: In a simply connected domain every harmonic function has its conjugate?

I am not able to get an example to disprove the statement.

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What is the converse? Please state it explicitly. –  timur Aug 24 '12 at 20:36
Let $u:\Omega\subseteq \mathbb{C}\rightarrow \mathbb{R}$ be harmonic and has conjugate, does it imply $\Omega$ is simply connected? –  miosaki Aug 24 '12 at 20:38
$\Omega$ is simply connected if every real harmonic function on $\Omega$ has a conjugate. –  Jonas Meyer Aug 24 '12 at 20:49
Do you have any idea about the other converse? If every harmonic function on a domain $\Sigma$ has a conjugate then $\Sigma$ is simply connected. –  JSchlather Aug 24 '12 at 21:22