Affine and linear invariant families of harmonic mappings
  We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk and determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class $\mathcal{S}_H$ of univalent harmonic mappings can be formulated as a question about Schwarzian norm and, in particular, our result shows consistency between the conjectured order of $\mathcal{S}_H$ and the Schwarzian norm of the harmonic Koebe function. 
Martin Chuaqui, Rodrigo Hern\'andez and Mar\'ia Jos\'e Mart\'in
math.CV