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 $\\zeta$ anda 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 pointsin the unit disc with non-negative imaginary part).

References

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

单词	FreeAnalyticBoundaryArc
释义	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 $\\zeta$ anda 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 pointsin the unit disc with non-negative imaginary part). References 1 John B. Conway..Springer-Verlag, New York, New York, 1995.
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