Title | Determination of the maximum of a product of inner radii of pairwise nonoverlapping domains |
Publication Type | Journal Article |
Year of Publication | 2016 |
Authors | Zabolotnij, Ja.V |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2016.03.007 |
Issue | 3 |
Section | Mathematics |
Pagination | 7-13 |
Date Published | 3/2016 |
Language | Ukrainian |
Abstract | Dubinin's problem on nonoverlapping domains in the complex plane is considered, and its solution for $\gamma\leq\sqrt{n}$ is obtained.
|
Keywords | inner radius, nonoverlapping domains, quadratic differential |
References:
- Lavrent'ev M. A. Tr. Fiz.-mat. inst. AN SSSR, 1934, 5: 195–245 (in Russian).
- Goluzin G. M. Geometric Theory of Functions of a Complex Variable, Translations of Mathematical Monographs, No 26, Amer. Math. Soc., Providence, R. I., 1969.
- Hayman W. K. Multivalent functions, Moscow: Izd-vo Inostr. lit., 1960 (in Russian).
- Jenkins J. A. Univalent functions and conformal mapping, Ergeb. Math. Grenzgeb. Neue Folge, Vol. 18, Reihe: Moderne Funktiontheorie, Springer-Verlag, 1958.
- Kolbina L. I. Vestnik Leningr. univ., 1955, 5: 37–43 (in Russian).
- Kuzmina G. V. Zap. Nauchn. Semin. POMI, 2001, 276: 253–275 (in Russian).
- 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.
- 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
- 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).
- Bakhtin A. K. Dopov. Nac. akad. nauk Ukr., 2006, No 10: 7–13 (in Russian).
- Bakhtin A. K. Ukr. Mat. Zh., 2009, 61, No 5: 596–610 (in Ukrainian). https://doi.org/10.1007/s11253-009-0247-4
- Podvisotskiy R. V. Dopov. Nac. akad. nauk Ukr., 2009, No 12: 33–37 (in Russian).
- Kovalev L. V. Russian Math. (Iz. VUZ), 2000, 44: 77–78 (in Russian).