  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.
