Inequalities for inner radii of symmetric disjoint domains

  • A. K. Bakhtin
  • L.V. Vyhovs'ka
  • I. V. Denega

Abstract

We study the following problem: Let a0=0,|a1|=...=|an|=1,akBkC, where B0,...,Bn are disjoint domains, and B1,...,Bn are symmetric about the unit circle. It is necessary to find the exact upper bound for rγ(B0,0)nk=1r(Bk,ak), where r(Bk,ak) is the inner radius of Bk with respect to ak. For γ=1 and n2, the problem was solved by L. V. Kovalev. We solve this problem for γ(0,γn],γn=0,38n2, and n2 under the additional assumption imposed on the angles between the neighboring line segments [0,ak].
Published
25.09.2018
How to Cite
Bakhtin, A. K., L. Vyhovs’ka, and I. V. Denega. “Inequalities for Inner Radii of Symmetric disjoint domains”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 9, Sept. 2018, pp. 1282-8, https://umj.imath.kiev.ua/index.php/umj/article/view/1634.
Section
Short communications