Geodesic
Holomorphic motions and uniformization of holomorphic families of Riemann surfaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 6, pp. 1091-1165

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Sufficient conditions for the simultaneous uniformization of holomorphic families of Riemann surfaces are investigated. The main method is based on a local construction of holomorphic and almost holomorphic motions with subsequent use of the machinery of Teichmüller spaces. Holomorphic motions are also applied to the closely related problem of extending a complex structure. Bibliography: 62 titles.
Keywords: Riemann surfaces, Teichmüller spaces, uniformization, holomorphic motions, removable singularities. 
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     author = {E. M. Chirka},
     title = {Holomorphic motions and uniformization of holomorphic families of {Riemann} surfaces},
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E. M. Chirka. Holomorphic motions and uniformization of holomorphic families of Riemann surfaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 6, pp. 1091-1165. http://geodesic.mathdoc.fr/item/RM_2012_67_6_a4/