
doi: 10.1007/bf02921638
This paper discusses the problem of natural extensions of holomorphic motions; it gives the following unique way of extensions. Let \(\overline{D}\) be the closed unit disc and \(\{X_z ; z\in \overline{D}\}\), a real analytic family of the real analytic plane Jordan curves \(X_z\). If \(j_p\), \(p\in \partial D\), is a real analytic family of orientation-reversing homeomorphisms of the Riemann sphere that fix the curve \(X_p\) pointwise, then there is a unique holomorphic motion of the Riemann sphere extending the given motion of Jordan curves and consistent with the family of homeomorphisms \(\{j_p\}\).
holomorphic families of domains, holomorphic motion, reflection principle, Teichmüller theory for Riemann surfaces
holomorphic families of domains, holomorphic motion, reflection principle, Teichmüller theory for Riemann surfaces
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