Charatheodory and Smirnov type theorem for harmonic mappings

Abstract

We prove a version of Smirnov type theorem and Charatheodory type theorem for a harmonic homeomorphism of the unit disk onto a Jordan surface with rectifiable boundary. Further we establish the classical isoperimetric inequality and Riesz--Zygmund inequality for Jordan harmonic surfaces without any smoothness assumptions of the boundary.

This manuscript contains substantial difference with the previous submission