Conformally natural extension of homeomorphisms of the circle

Ahlfors, L. V.,Lectures on quasiconformal mappings. Van Nostrand-Reinhold, Princeton, 1966.

Ahlfors, L. V. &Bers, L., Riemann’s mapping theorem for variable metrics.Ann. of Math., 72 (1960), 385–404.

Bers, L.,On moduli of Riemann surfaces. Lecture notes, E.T.H., Zürich, 1964.

—, Automorphic forms and general Teichmüller spaces, inProceedings of the Conference on Complex Analysis (Minneapolis 1964), pp. 109–113. Springer, Berlin, 1965.

—, Finite dimensional Teichmüller spaces and generalizations.Bull. Amer. Math. Soc., 5 (1981), 131–172.

Beurling, A. &Ahlfors, L. V., The boundary correspondence under quasiconformal mappings.Acta Math., 96 (1956), 125–142.

Choquet, G., Sur un type de transformation analytique généralisant la réprésentation conforme et définie au moyen de fonctions harmoniques.Bull. Sci. Math. (2), 69 (1945), 156–165.

Earle, C. J., The Teichmüller space of an arbitrary Fuchsian group.Bull. Amer. Math. Soc., 70 (1964), 699–701.

—, The contractability of certain Teichmüller spaces.Bull. Amer. Math. Soc., 73 (1967), 434–437.

—, On quasiconformal extensions of the Beurling-Ahlfors type, inContributions to Analysis, pp. 99–105. Academic Press, New York, 1974.

Earle, C. J. &Eells, J., On the differential geometry of Teichmüller spaces.J. Analyse Math., 19 (1967), 35–52.

Kneser, H., Lösung der Aufgabe 41.Jahresber. Deutsch. Math.-Verein., 35 (1926), 123–124.

Lehto, O. &Virtanen, K. I.,Quasiconformal mappings in the plane. Springer, Berlin and New York, 1973.

Lehtinen, M., Remarks on the maximal dilatation of the Beurling-Ahlfors extension.Ann. Acad. Sci. Fenn. Ser. A I Math., 9 (1984), 133–139.

Tukia, P., On infinite dimensional Teichmüller spaces.Ann. Acad. Sci. Fenn Ser. A I Math., 3 (1977), 343–372.

—, Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group.Acta Math., 154 (1985), 153–193.