Generalized harmonic Koebe functions
  We present a family of sense-preserving harmonic mappings in the unit disk related to the classical generalized (analytic) Koebe functions. We prove that these are precisely the mappings that maximize simultaneously the real part of every Taylor coefficient as well as the growth and distortion of functions in affine and linear invariant families of complex-valued harmonic functions. 
\'Alvaro Ferrada-Salas and Mar\'ia J. Mart\'in
math.CV