Continuations of a Riemann surface and dynamics of viscos fluid --- study of conformal embeddings and associated Poiseuille flow

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Along the study of conformal embedding of an open Riemann surface into a closed surface of the same genus we encountered with interesting fuctions on a closed disk. The functions are written in terms ofthe euclidean and hyperbolic (resp.spherical) metrics, in case of genus one (resp. zero). .In the present research project we studied these functions from the hydrodymanic viewpoint and showed that they represent Poiseuille flows. We also gave the viscosity in closed forms.