About the product if inner radii of pairwise non-overlapping domains

A.K. Bakhtin. Scientific legacy

“…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.…”

Sharp estimates of products of inner radii of non-overlapping domains in the complex plane

“…This problem belongs to the class of extremal problems with free poles. Problems of this type have been studied in many papers (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]). For γ = 1 2 and n 2, an estimate of the functional J n (γ) for the system of non-overlapping domains was found in the paper [6, p. 59].…”

“…Note that for n = 2 the Kuz'mina's estimate of the functional (1) coincides with the Dubinin's estimate. Some partial cases of the above-posed problem were considered in [2,3,5].…”