free analytic boundary arc

Definition.

Let $G\subset\mathbb{C}$ be a region and let $\gamma$ be a connected subset of $\partial G$ (boundary of $G$ ), then $\gamma$ is a free analytic boundary arc of $G$ if for every point $\zeta\in\gamma$ there is a neighbourhood $U$ of $\zeta$ and a conformal equivalence $h\colon{\mathbb{D}}\to U$ (where ${\mathbb{D}}$ is the unit disc) such that $h(0)=\zeta$ , $h(-1,1)=\gamma\cap U$ and $h({\mathbb{D}}_{+})=G\cap U$ (where ${\mathbb{D}}_{+}$ is all the points in the unit disc with non-negative imaginary part).

References

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

Title	free analytic boundary arc
Canonical name	FreeAnalyticBoundaryArc
Date of creation	2013-03-22 14:18:00
Last modified on	2013-03-22 14:18:00
Owner	jirka (4157)
Last modified by	jirka (4157)
Numerical id	7
Author	jirka (4157)
Entry type	Definition
Classification	msc 30-00
Classification	msc 54-00
Related topic	AnalyticCurve