A Sharp Condition for the Loewner Equation to Generate Slits

D. Marshall and S. Rohde have recently shown that there exists $C_0>0$ so that the Loewner equation generates slits whenever the driving term is H"older continuous with exponent 1/2 and norm less than $C_0$. In this paper, we show that the maximal value for $C_0$ is 4.