Chordal Loewner equation

For a capacity-parameterized locally growing hull family,where the continuous real function $U$ is the Loewner driving function.

The Loewner driving function $U_t$ is the real boundary point at which the mapped-out hull grows. Scaling the hulls by $a^{-1}$ and time by $a^2$ transforms it to $a^{-1}{U}_{a^{2}t}$.