The Moutard transformation of two-dimensional Dirac operators and the   Mobius geometry
  We describe the action of the (Mobius) inversion on the data of the Weierstrass representation of surfaces in the three-space and show that the Moutard transformation of two-dimensional Dirac operators has a geometrical meaning: it maps the potential $U$ of a surface $S$ into the potential of its inversion. 
Iskander A. Taimanov
math.DG nlin.SI