Determination of the maximum of a product of inner radii of pairwise nonoverlapping domains

TitleDetermination of the maximum of a product of inner radii of pairwise nonoverlapping domains
Publication TypeJournal Article
Year of Publication2016
AuthorsZabolotnij, Ja.V
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2016.03.007
Issue3
SectionMathematics
Pagination7-13
Date Published3/2016
LanguageUkrainian
Abstract
Dubinin's problem on nonoverlapping domains in the complex plane is considered, and its solution for $\gamma\leq\sqrt{n}$ is obtained.
Keywordsinner radius, nonoverlapping domains, quadratic differential
References: 
  1. Lavrent'ev M. A. Tr. Fiz.-mat. inst. AN SSSR, 1934, 5: 195–245 (in Russian).
  2. Goluzin G. M. Geometric Theory of Functions of a Complex Variable, Translations of Mathematical Monographs, No 26, Amer. Math. Soc., Providence, R. I., 1969.
  3. Hayman W. K. Multivalent functions, Moscow: Izd-vo Inostr. lit., 1960 (in Russian).
  4. Jenkins J. A. Univalent functions and conformal mapping, Ergeb. Math. Grenzgeb. Neue Folge, Vol. 18, Reihe: Moderne Funktiontheorie, Springer-Verlag, 1958.
  5. Kolbina L. I. Vestnik Leningr. univ., 1955, 5: 37–43 (in Russian).
  6. Kuzmina G. V. Zap. Nauchn. Semin. POMI, 2001, 276: 253–275 (in Russian).
  7. Dubinin V. N. Uspekhi mat. nauk., 1994, 49, No 1: 3–76 (in Russian); translation in Russian Math. Surveys, 1994, 49, No 1: 1–79.
  8. Dubinin V. N. Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklov (LOMI), 1988, 168: 48–66 (in Russian); translation in J. Soviet Math., 1991, 53, No 3: 252–263. https://doi.org/10.1007/BF01303649
  9. Bakhtin A. K., Bakhtina G. P., Zelinskii Yu. B. Topological-algebraic structures and geometric methods in complex analysis, Proc. of the Institute of Mathematics of the NAS of Ukraine, Kyiv, 2008 (in Russian).
  10. Bakhtin A. K. Dopov. Nac. akad. nauk Ukr., 2006, No 10: 7–13 (in Russian).
  11. Bakhtin A. K. Ukr. Mat. Zh., 2009, 61, No 5: 596–610 (in Ukrainian). https://doi.org/10.1007/s11253-009-0247-4
  12. Podvisotskiy R. V. Dopov. Nac. akad. nauk Ukr., 2009, No 12: 33–37 (in Russian).
  13. Kovalev L. V. Russian Math. (Iz. VUZ), 2000, 44: 77–78 (in Russian).