Conformally natural reflections in Jordan curves with applications to Teichmüller spaces
In his fundamental paper  Ahlfors initiated the study of quasiconformal reflections. Using the results of Beurling and Ahlfors  he showed that every quasicircle that passes through ∞ permits a quasiconformal reflection that satisfies a global Lipschitz condition (with exponent one) in the plane. Using that result he proved by a direct construction that the Bers embedding of the universal Teichmüller space has an open image. Lipschitz continuous quasiconformal reflections also play a crucial role in Bers’s subsequent proof (see  and ) that for any Teichmüller space the Bers embedding not only has an open image but also has local cross sections. That result is one of the cornerstones of Teichmüller theory.
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