Hilbert uniformization at string coffee table
C.-F. Bödigheimer, Configuration models for moduli spaces of Riemann surfaces with boundary, Abh. Math. Sem. Univ. Hamburg 76 (2006), 191–233.
C.-F. Bödigheimer, Hilbert uniformaization of Riemann surfaces: I (2004),pdf
C.-F. Bödigheimer, Moduli spaces of Riemann surfaces with boundary (2003).
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