It is proved that every quasiconfomal harmonic mapping of the unit disk onto a surface with rectifiable boundary has absolutely continuous extension to the boundary as well as its inverse mapping has this property. In addition it is proved an isoperimetric type inequality for the class of these surfaces. These results extend some classical results for conformal mappings, minimal surfaces and surfaces with constant mean curvature treated by Kellogg, Courant, Nitsche, Tsuji, F. Riesz and M. Riesz, etc.
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