Holomorphic motions and uniformization of holomorphic families of Riemann surfaces

E. M. Chirka

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 6, pp. 1091-1165

Résumé

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.

Détail

Keywords: Riemann surfaces, uniformization, holomorphic motions, removable singularities.
Mots-clés : Teichmüller spaces

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