Radial segments and conformal mapping of an annulus onto domains bounded by a circle and a k-circle
Volume 56 / 1992
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 $φ_2$ $(0 ≤ φ_1 ≤ φ_2 ≤ 2π)$.
