Generalized M.A. Lavrentiev’s inequality

Bootstrapping closed string field theory

“…where r i is the mapping radius of the map from unit disk 0 < |w i | ≤ 1 to the face of the critical graph the puncture at z = ξ i belongs. As a matter of fact, (1.6) has been rigorously proved in geometric function theory [32][33][34][35][36][37], but appears to have been unnoticed in physics literature; here we rediscovered it. We test (1.6) against some of the known cases of Strebel differentials in section 3.…”

A.K. Bakhtin. Scientific legacy

“…In [9] there were proposed a method allowing to obtain new estimates for the products of inner radii of mutually non-overlapping domains. In particular, it allowed to generalize and strengthen the result of M. A. Lavrentiev [36] on the maximum of product of conformal radii of two non-overlapping simply connected domains.…”

“…Theorem 6.1. [9] Let n P N. Then, for any fixed system of mutually distinct points ta k u n k=1 P Czt0u and any mutually non-overlapping domains tB k u n k=0 , a k P B k Ă C, k = 0, n, a 0 = 0, the following inequality holds r n (B 0 , 0) On the other hand, provided all conditions of Corollary 6.2, from the M. A. Lavrentiev' Theorem 3.1, we obtain the inequality r(B 0 , 0)r(B k , a k ) ď ρ 2 , k = 1, n.…”

“…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.…”

Application of upper estimates for products of inner radii to distortion theorems for univalent functions

“…No other ultimate results in this problem for n ⩾ 5 are known at present. In 2021 [4,15] effective upper estimates are obtained for T n , n ⩾ 2. Among the possible applications of the obtained results in other tasks of the function theory are the so-called distortion theorems.…”