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Page 9 - It is not too difficult to go from the representation formula to the existence theorem. The existence theorem for quasiconformal mappings, more recently called the "measurable Riemann mapping theorem...
Page 6 - Thus the generalisation to Sobolev spaces is necessary if one is to solve extremal problems. We then find the limit of a bounded sequence of quasiconformal mappings is either quasiconformal or constant. The equivalence between the geometric definition and the analytic definition was shown by F. W.
Page ix - The first author was supported in part by grants from the US National Science Foundation. The...
Page 89 - K. Astala, Area distortion of quasiconformal mappings, Acta Math., 173, (1994), 37-60.
Page 91 - T. Iwaniec and V. Sverak, On mappings with integrable dilatation, Proc. Amer. Math. Soc., 118, (1993), 181-188.
Page 89 - LV Ahlfors, Lectures on quasiconformal mappings, Van Nostrand, Princeton 1966; Reprinted by Wadsworth Inc. Belmont, (1987).