Radial segments and conformal mapping of an annulus onto domains bounded by a circle and a k-circle

• Autorzy: Tetsuo Inoue
• Języki publikacji: EN

Abstrakty

EN

Let f(z) be a conformal mapping of an annulus A(R) = {1 < |z| < R} and let f(A(R)) be a ring domain bounded by a circle and a k-circle. If R(φ) = {w : arg w = φ}, and l(φ) - 1 is the linear measure of f(A(R)) ∩ R(φ), then we determine the sharp lower bound of $l(φ_1) + l(φ_2)$ for fixed $φ_1$ and $φ_2$ $(0 ≤ φ_1 ≤ φ_2 ≤ 2π)$.

Kategorie tematyczne

• 30C25: Covering theorems in conformal mapping theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991-1992
• Tom: 56
• Numer: 2
• Strony: 157-162

Daty

wydano

1992

otrzymano

1990-10-22

poprawiono

1991-04-22

Twórcy

autor

Tetsuo Inoue

• Department of Applied Mathematics, Kobe University of Mercantile Marine, Fukae Minamimachi 5-1-1, Higashinada-ku, Kobe, Japan 658

Bibliografia

• [1] L. V. Ahlfors, Quasiconformal reflections, Acta Math. 109 (1963), 291-301.
• [2] D. K. Blevins, Conformal mappings of domains bounded by quasiconformal circles, Duke Math. J. 40 (1973), 877-883.
• [3] D. K. Blevins, Harmonic measure and domains bounded by quasiconformal circles, Proc. Amer. Math. Soc. 41 (1973), 559-564.
• [4] D. K. Blevins, Covering theorems for univalent functions mapping onto domains bounded by quasiconformal circles, Canad. J. Math. 28 (1976), 627-631.
• [5] W. K. Hayman, Multivalent Functions, Cambridge Univ. Press, 1958.
• [6] J. A. Jenkins, Some uniqueness results in the theory of symmetrization, Ann. of Math. 61 (1955), 106-115.
• [7] O. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, second ed., Springer, 1973.
• [8] I. P. Mityuk, Principle of symmetrization for the annulus and some of its applications, Sibirsk. Mat. Zh. 6 (1965), 1282-1291 (in Russian).