Loewner chain

A Loewner chain is a continuous function $f:𝔻\times [0,\mathrm{\infty })\to ℂ$ (where $𝔻$ refers to the open unit disc) with the following properties:

1. the function $z\mapsto f(z,t)$ is analytic and univalent for all $t\in [0,\mathrm{\infty })$

2. $f(0,t)=0$ and $f^{\prime }(0,t)=e^t$

3. $f(𝔻,s)\subseteq f(𝔻,t)$ for

Bibliography

• John B. Conway . Springer-Verlag, New York, Inc, 1995