Let $S$ be a riemann surface.If 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 $S$.And S$. Also this metric is the same as can be derived from the restriction to$S$of the poincare metric of$S^N$,where$S^N$is the Nielsen extension of$S$.So S$.I don't know what is the Nielsen extension ?of $S$ is
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 $S$.And this metric is the same as the restriction to $S$ of the poincare metric of $S^N$,where $S^N$ is the Nielsen extension of $S$.So what is the extension?