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

Annales Polonici Mathematici (1992)

- Volume: 56, Issue: 2, page 157-162
- ISSN: 0066-2216

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topTetsuo Inoue. "Radial segments and conformal mapping of an annulus onto domains bounded by a circle and a k-circle." Annales Polonici Mathematici 56.2 (1992): 157-162. <http://eudml.org/doc/262294>.

@article{TetsuoInoue1992,

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)$.},

author = {Tetsuo Inoue},

journal = {Annales Polonici Mathematici},

keywords = {Koebe region; chordal cross ratio; -circle},

language = {eng},

number = {2},

pages = {157-162},

title = {Radial segments and conformal mapping of an annulus onto domains bounded by a circle and a k-circle},

url = {http://eudml.org/doc/262294},

volume = {56},

year = {1992},

}

TY - JOUR

AU - Tetsuo Inoue

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

JO - Annales Polonici Mathematici

PY - 1992

VL - 56

IS - 2

SP - 157

EP - 162

AB - 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)$.

LA - eng

KW - Koebe region; chordal cross ratio; -circle

UR - http://eudml.org/doc/262294

ER -

## References

top- [1] L. V. Ahlfors, Quasiconformal reflections, Acta Math. 109 (1963), 291-301. Zbl0121.06403
- [2] D. K. Blevins, Conformal mappings of domains bounded by quasiconformal circles, Duke Math. J. 40 (1973), 877-883. Zbl0275.30015
- [3] D. K. Blevins, Harmonic measure and domains bounded by quasiconformal circles, Proc. Amer. Math. Soc. 41 (1973), 559-564. Zbl0281.30015
- [4] D. K. Blevins, Covering theorems for univalent functions mapping onto domains bounded by quasiconformal circles, Canad. J. Math. 28 (1976), 627-631. Zbl0362.30013
- [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. Zbl0064.07501
- [7] O. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, second ed., Springer, 1973. Zbl0267.30016
- [8] I. P. Mityuk, Principle of symmetrization for the annulus and some of its applications, Sibirsk. Mat. Zh. 6 (1965), 1282-1291 (in Russian).

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