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Quanting Zhao
Quanting Zhao
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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 Also this metric is the same ascan be derived from the restriction to $S$ of the poincare metric of $S^N$,where $S^N$ is the Nielsen extension of $S$.SoI 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?

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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Quanting Zhao
Quanting Zhao
  • 93
  • 7

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 $S$.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?