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Rodin, Burton; Warschawski, Stefan E.

Extremal length and univalent functions. I: The angular derivative. (English) Zbl 0384.30006

Math. Z. 153, 1-17 (1977).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 4 Reviews
Cited in 13 Documents

MSC:

30C75 Extremal problems for conformal and quasiconformal mappings, other methods
30C35 General theory of conformal mappings
30C85 Capacity and harmonic measure in the complex plane
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
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Full Text: DOI EuDML

References:

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[2] Ahlfors, L.V.: Conformal invariants: Topics in geometric function Theory. New York: McGraw-Hill 1973 · Zbl 0272.30012
[3] Eke, B.G.: On the differentiability of conformal maps at the boundary. Nagoya math. J.41, 43-53 (1971) · Zbl 0181.08402
[4] Eke, B.G.: Comparison domains for the problem of the angular derivative. Commentarii math. Helvet.46, 43-53 (1971) · Zbl 0207.07705 · doi:10.1007/BF02566830
[5] Ferrand, J.: Sur l’inégalité d’Ahlfors et son application au problème de la dérivée angulaire. Bull. Soc. math. France72, 178-192 (1944) · Zbl 0060.23304
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[9] Jenkins, A.J., Oikawa, K.: On results of Ahlfors and Hayman. Illinois J. Math.15, 664-671 (1971) · Zbl 0229.30012
[10] Jenkins, J.A., Oikawa, K.: Conformality and semi-conformality at the boundary.J. reine angew. Math. (To appear) · Zbl 0339.30024
[11] Knopp, K.: Theorie und Anwendung der unendlichen Reihen. 5th ed. Berlin-Heidelberg-New York: Springer 1964 · Zbl 0124.28302
[12] Löwner, K.: Untersuchungen über schlichte konforme Abbildungen des Einheitskreises I. Math. Ann.89, 103-121 (1923) · JFM 49.0714.01 · doi:10.1007/BF01448091
[13] Montel, P.: Sur la représentation conforme. J. Math. pur. appl., Ser. VII3, 1-54 (1917) · JFM 46.0548.03
[14] Obrock, A.E.: On bounded oscillation and asymptotic expansion of conformal strip mappings. Trans. Amer. math. Soc.173, 183-201 (1972) · Zbl 0256.30007 · doi:10.1090/S0002-9947-1972-0310214-4
[15] Oikawa, K.: On angular dervatives of univalent functions. Kodai math. Sem. Reports27, 193-210 (1976) · Zbl 0341.30010 · doi:10.2996/kmj/1138847176
[16] Ostrowski, A.: Zur Randverzerrung bei konformer Abbildung. Prace mat.-fiz.44, 371-471 (1936) · Zbl 0020.23802
[17] Rodin, B., Warschawski, S.E.: Extremal length and the boundary behavior of conformal mappings. Ann. Acad. Sci. Fennicae, Ser. A I. (To appear) · Zbl 0348.30007
[18] Teichmüller, O.: Untersuchungen über konforme und quasikonforme Abbildung. Deutsche Math.3, 621-678 (1938) · Zbl 0020.23801
[19] Warschawski, S. E.: On conformal mapping of infinite strips. Trans. Amer. math. Soc.51, 280-355 (1942) · Zbl 0028.40303
[20] Warschawski, S.E.: On the boundary behavior of conformal maps. Nagoya math. J.30, 83-101 (1967) · Zbl 0179.39402
[21] Warschawski, S.E.: Remarks on the angular derivative. Nagoya math. J.41, 19-32 (1971) · Zbl 0209.11002
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