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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”.

##### MSC:
 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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