Loewner chain

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

1.

the function $z\mapsto f(z,t)$ is analytic and univalent for all $t\in[0,\infty)$
2.

$f(0,t)=0$ and $f^{\prime}(0,t)=e^{t}$
3.

$f({\mathbb{D}},s)\subseteq f({\mathbb{D}},t)$ for $0\leq s<t<\infty$

Bibliography

•

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

Title	Loewner chain
Canonical name	LoewnerChain
Date of creation	2013-03-22 14:12:02
Last modified on	2013-03-22 14:12:02
Owner	jirka (4157)
Last modified by	jirka (4157)
Numerical id	4
Author	jirka (4157)
Entry type	Definition
Classification	msc 30C55