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Ahlfors--Weill Extension, Asymptotically Conformal Curves and Epstein--Poincaré Surfaces
The Ahlfors--Weill construction explicitly extends a univalent function $f$ with Schwarzian norm less than $1/2$ to a quasiconformal homeomorphism of the Riemann sphere, an extension that can be understood geometrically through Epstein surfaces. For asymptotically conformal curves, the uniformizatio
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