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

Volume 56 / 1992

Tetsuo Inoue Annales Polonici Mathematici 56 (1992), 157-162 DOI: 10.4064/ap-56-2-157-162

Abstract

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 $φ_2$ $(0 ≤ φ_1 ≤ φ_2 ≤ 2π)$.

Authors

  • Tetsuo Inoue

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