Sufficient conditions in the two-functional conjecture for univalent   functions
  The two-functional conjecture says that if a function f analytic and univalent in the unit disk maximizes Re{L} and Re{M} for two continuous linear functionals L and M, L is not equal to cM for any c>0, then f is a rotation of the Koebe function. We use the Loewner differential equation to obtain sufficient conditions in the two-functional conjecture and compare the sufficient conditions with necessary conditions. 
Dmitri Prokhorov
math.CV