# Nielsen extension of Riemann surface

Let $S$ be a riemann surface. If S has idea boundary curves,then the intrinsic metric on $S$ can be defined by the restriction to $S$ of poincare metric of the double of $S$. Also this metric can be derived from the restriction to $S$ of the poincare metric of $S^N$,where $S^N$ is the Nielsen extension of $S$.I don't know what the Nielsen extension of $S$ is

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I suggest you rewrite the question as follows: 'What is the Nielsen extension of a Riemann surface?' – HJRW Jan 4 '11 at 15:55
OK,I see.Thank you for your advice – Quanting Zhao Jan 5 '11 at 6:49