Holomorphic motions and Teichmüller spaces

Earle, C. J.; Kra, I.; Krushkal′, S. L.

doi:10.1090/S0002-9947-1994-1214783-6

Holomorphic motions and Teichmüller spaces
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by C. J. Earle, I. Kra and S. L. Krushkal′ PDF

Trans. Amer. Math. Soc. 343 (1994), 927-948 Request permission

Abstract:

We prove an equivariant form of Slodkowski’s theorem that every holomorphic motion of a subset of the extended complex plane $\hat {\mathbb {C}}$ 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.

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Prolongement de mouvements holomorphes

d’après Slodkowski et autres