On harmonic quasiconformal immersions of surfaces in $\mathbb{R}^3$
  This paper is devoted to the study of the global properties of harmonically immersed Riemann surfaces in $\mathbb{R}^3.$ We focus on the geometry of complete harmonic immersions with quasiconformal Gauss map, and in particular, of those with finite total curvature. We pay special attention to the construction of new examples with significant geometry. 
Antonio Alarcon and Francisco J. Lopez
math.DG