Boundary Behaviour of Conformal Maps pp 18-40 | Cite as
Continuity and Prime Ends
Chapter
Abstract
Let f map the unit disk D conformally onto \( G \subset \hat {\Bbb C} = {\Bbb C} \cup \left\{ \infty \right\}\). In this chapter, we study the problem whether it is possible to extend f to some or all points ζ ∈ T = ∂D by defining
$$ f\left( \zeta \right) = \mathop {\lim }\limits_{z \to \zeta } f\left( z \right) \in \hat {\Bbb C}.$$
(1)
Keywords
Jordan Curve Junction Point Jordan Domain Radial Limit Angular Limit
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© Springer-Verlag Berlin Heidelberg 1992