Loewner differential equation

Summary

The Loewner differential equation describes a family of conformal maps that change continuously in time. Each map sends the complement of a growing set onto a fixed reference domain. The whole family is driven by a single real or circle-valued function of time, the driving function. Charles Loewner introduced it to prove the case $n = 3$ of the Bieberbach conjecture. Louis de Branges used it in the proof of the full conjecture. With a Brownian motion as driving function it defines the Schramm–Loewner evolution.