A univalent function nowhere semiconformal on the unit circle

Yamashita, Shinji

doi:10.1090/S0002-9939-1978-0466525-6

A univalent function nowhere semiconformal on the unit circle
HTML articles powered by AMS MathViewer

by Shinji Yamashita PDF

Proc. Amer. Math. Soc. 69 (1978), 85-86 Request permission

Abstract:

We shall construct a function f holomorphic and univalent in the open unit disk such that f is not semiconformal at any point of the unit circle. It is also shown that f may be extended quasiconformally to the whole extended plane.

References

Jochen Becker, Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen, J. Reine Angew. Math. 255 (1972), 23–43 (German). MR 299780, DOI 10.1515/crll.1972.255.23
D. M. Campbell and J. A. Pfaltzgraff, Boundary behaviour and linear invariant families, J. Analyse Math. 29 (1976), 67–92. MR 477054, DOI 10.1007/BF02789976
Peter A. Lappan, Fatou points of harmonic normal functions and uniformly normal functions, Math. Z. 102 (1967), 110–114. MR 222265, DOI 10.1007/BF01112077
Christian Pommerenke, Linear-invariante Familien analytischer Funktionen. I, II, Math. Ann. 155 (1964), 108–154; ibid. 156 (1964), 226–262 (German). MR 0168751, DOI 10.1007/BF01363289
Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
C. Visser, Über beschränkte analytische Funktionen und die Randverhältnisse bei konformen Abbildungen, Math. Ann. 107 (1933), no. 1, 28–39 (German). MR 1512784, DOI 10.1007/BF01448877
J. L. Walsh and D. Gaier, Zur Methode der variablen Gebiete bei der Randverzerrung, Arch. Math. (Basel) 6 (1954), 77–86 (German). MR 64874, DOI 10.1007/BF01899218