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I have a rather straightforward and perhaps somewhat naive question: Is there a Teichmüller theory for open surfaces? My motivation basically is that I would like to find out more about the "...

I have read in some papers about Rauch-type variational formulas on Hurwitz spaces, and I would like to know what exactly is the theory behind them. A Hurwitz Space $H_g^d$ is the space of coverings ...