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We prove representation theorems, the versions of Smirnov's theorem and Caratheo- dory type theorem for harmonic homeomorphisms of the unit disk onto Jordan surfaces with rectifi- able boundaries. Further we establish the classical isoperimetric inequality and the Riesz-Zygmund inequality for Jordan harmonic surfaces without any smoothness assumptions on the boundary.

Carathéodory and Smirnov type theorems for harmonic mappings of the unit disk onto surfaces