Charatheodory and Smirnov type theorem for harmonic mappings
  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. 
David Kalaj, Marijan Markovic, Miodrag Mateljevic
math.CV math.DG