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Normal Functions and Non-Tangential Boundary Arcs

Published online by Cambridge University Press:  20 November 2018

P. Lappan  and
D. C. Rung
P. Lappan
Affiliation:
Lehigh University and Pennsylvania State University
D. C. Rung
Affiliation:
Lehigh University and Pennsylvania State University
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Let D and C denote respectively the open unit disk and the unit circle in the complex plane. Further, γ = z(t), 0 ⩽ t ⩽ 1, will denote a simple continuous arc lying in D except for Ƭ = z(l) ∈ C, and we shall say that γ is a boundary arc at Ƭ.

We use extensively the notions of non-Euclidean hyperbolic geometry in D and employ the usual metric

where a and b are elements of D. For a ∈ D and r > 0 let

For details we refer the reader to (4).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 256 - 264
Copyright
Copyright © Canadian Mathematical Society 1966

References

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