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On the boundary
continuity of conformal maps
Christian Pommerenke |
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Vol. 120 (1985), No. 2, 423–430
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Abstract |
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Let the function f map the unit disk D conformally onto the domain G in C = C ∪{∞} . The prime end theory of Carathéodory gives a completely geometric characterization of the boundary behavior of f. Prime ends are defined in terms of crosscuts of G. Our aim is to give a geometric description of the boundary behavior of f that refers only to the boundary ∂G and not to the domain itself. It can therefore be applied to any complementary domain of a connected closed set in C. Our description will however be incomplete because we will have to allow exceptional sets. |
Mathematical Subject Classification 2000
Primary: 30C20
Secondary: 30D40
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Milestones
Received: 6 July 1984
Published: 1 December 1985
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Authors |
| Christian Pommerenke | |
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