Problem on extremal decomposition of the complex plane with free poles

Abstract

We consider the well-known problem of the geometric theory of functions of a complex variable on non-overlapping domains with free poles on radial systems. The main results of the present work strengthen and generalize several known results for this problem.

A.K. Bakhtin. Scientific legacy

“…A general approach is proposed that allows to transfer most of the results of geometric function theory to the case of an arbitrary multidimensional complex space C n , n ě 2 [3,4]. An effective upper estimates are obtained for the products of inner radii of mutually non-overlapping domains with fixed poles corresponding quadratic differentials [10]. An open problem of finding the maximum of product of inner radii of two domains relative to the points of a unit circle with each power γ P (0, 2 ] of the inner radius of the domain relative to the origin, provided that all three domains are mutually non-overlapping domains is solved.…”

“…Under the O. K. Bakhtin supervision A. L. Targonskyi (2006) [12][13][14][41][42][43][44][45], V. E. Vyun (2008) [17][18][19], R. V. Podvisotskii [5,11], I. Y. Vygovska (2012) [46][47][48], I. V. Denega (2013) [7][8][9], Y. V. Zabolotnyi (2014) [20,22,26,27], L. V. Vyhivska (2019) [10,15,16], I. Y. Dvorak (2019) [10,21] defended their candidate theses.…”