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Holomorphic motions and Teichmüller spaces. (English) Zbl 0812.30018
Authors’ abstract: “We prove an equivariant form of Slodkowski’s theorem that every holomorphic motion of a subset of the extended complex plane \(\widehat{\mathbb{C}}\) extends to a holomorphic motion of \(\widehat{\mathbb{C}}\). As a consequence we prove that every holomorphic map of the unit disc into Teichmüller space lifts to a holomorphic map into the space of Beltrami forms. We use this lifting theorem to study the Teichmüller metric”.

30F60 Teichmüller theory for Riemann surfaces
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
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