On the Differentiability of Conformal Maps at the Boundary
- 1 February 1971
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 41, 43-53
- https://doi.org/10.1017/s0027763000014045
Abstract
Let S be a simply connected domain in the w + u + iv plane and let ∂S denote its boundary which we assume passes through w= ∞. Suppose that the segment L= {u ≧ u0; v = 0} of the real axis lies in S and that w∞ is the point of ∂ S accessible along L. Let z = z(w) = x(w) + iy(w) map S in a (1 — 1) conformal way onto ∑ = {z = x + iy: — ∞ < x < + ∞ } so that . The inverse map is w = w(z) = u(z) + iv(z). S is said to possess a finite angular derivative at w∞ if z(w) — w approaches a finite limit (called the angular derivative) as w→w∞ in certain substrips of S.Keywords
This publication has 3 references indexed in Scilit:
- On the Distortion of Conformal Maps at the BoundaryJournal of the London Mathematical Society, 1969
- On the Angular Derivative of Regular Functions.MATHEMATICA SCANDINAVICA, 1967
- On the Boundary Behavior of Conformal MapsNagoya Mathematical Journal, 1967