# 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 FreeAnalyticBoundaryArc 2013-03-22 14:18:00 2013-03-22 14:18:00 jirka (4157) jirka (4157) 7 jirka (4157) Definition msc 30-00 msc 54-00 AnalyticCurve