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We construct a global system of real analytic coordinates on the real Teichmuller space of a compact real algebraic curve X, using so-called strict uniformization of the real algebraic curve X. A global coordinate system is then obtained via real quasiconformal deformations of the Kleinian subgroup of PGL2(R) obtained as a group of covering transformations of a strict uniformization of X.

Strict uniformization of real algebraic curves and global real analytic coordinates on real Teichmülhler spaces