Well I was thinking on this problem, any idea to progress will be gladly accepted, Let $f:\Omega\rightarrow V$ be a biholomorphic map where $\Omega$ and $V$ are bounded open set in $\mathbb{C}$ Does $f$ extend continously to the boundary?
Extension of biholomorphic map to the boundary
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complex-analysis
1 Answers
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No, this is in general not true. Standard counterexamples occur on slit annuli $\{z: 1\le |z|\le R\}\backslash \{z: Im(z) = 0, Re(z) <0\}$ which cannot be extended periodically along on the circles $\{|z|=r\}$ (like, say, $\log$).
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0@Mex: sorry, can't help you with this one. – 2012-06-03