Geodesic
Semigroups of conformal mappings
Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 463-483 Cet article a éte moissonné depuis la source Math-Net.Ru

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Sets of conformal mappings distinguished by boundary conditions and forming semigroups with respect to the operation of composition are studied. A description of one-parameter semigroups is given, and a connection between them and semiflows is established. With each semigroup there is associated an evolution equation that is an analogue of the Lëwner equation known in the theory of univalent functions. Existence theorems are obtained for the evolution equations, and their approximation properties are studied. It is also established that each mapping of the semigroups under consideration can be represented as a shift along solutions of the corresponding evolution equation. Bibliography: 19 titles. 
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V. V. Goryainov. Semigroups of conformal mappings. Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 463-483. http://geodesic.mathdoc.fr/item/SM_1987_57_2_a10/

[1] Löwner K., “Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I”, Math. Ann., 89 (1923), 103–121 | DOI | MR | Zbl

[2] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

[3] Aleksandrov I. A., Parametricheskie prodolzheniya v teorii odnolistnykh funktsii, Nauka, M., 1976 | MR

[4] Pommerenke Ch., Univalent functions, Vandenhoeck and Ruprecht, Göttingen, 1975 | MR | Zbl

[5] Gutlyanskii V. Ya., “Parametricheskoe predstavlenie odnolistnykh funktsii”, DAN SSSR, 194 (1970), 750–753 | Zbl

[6] Ahlfors L. V., Conformal invariants, Topics in Geometric function theory, McGraw-Hill Book Company, New York et al., 1973 | MR | Zbl

[7] Goryainov V. V., “O nekotorykh svoistvakh reshenii uravneniya Levnera–Kufareva”, DAN USSR. Ser. A, 1978, no. 3, 207–210

[8] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M.-L., 1950

[9] Avkhadiev F. G., Aksentev L. A., “Osnovnye rezultaty v dostatochnykh usloviyakh odnolistnosti analiticheskikh funktsii”, UMN, 30:4 (1975), 3–60 | MR | Zbl

[10] Goluzin G. M., “O tipichno veschestvennykh funktsiyakh”, Matem. sb., 27(69) (1950), 201–218 | MR | Zbl

[11] Kodington E. A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii., IL, M., 1958

[12] Sansone Dzh., Obyknovennye differentsialnye uravneniya, t. 2, IL, M., 1954

[13] Goryainov V. V., “O skhodimosti odnoparametricheskikh semeistv analiticheskikh funktsii”, Voprosy metricheskoi teorii otobrazhenii i ee primenenie, Naukova dumka, Kiev, 1978, 13–24 | MR

[14] Rudin U., Funktsionalnyi analiz, Mir, M., 1975 | MR

[15] Edvards R., Funktsionalnyi analiz, Mir, M., 1969

[16] Branges L., A proof of the Bieberbach conjecture, Preprint LOMI. E-5–84, LOMI, Leningrad, 1984

[17] Goryainov V. V., “K parametricheskomu predstavleniyu odnolistnykh funktsii”, DAN SSSR, 245 (1979), 1038–1041 | MR | Zbl

[18] Aleksandrov I. A., Tsvetkov B. G., “Funktsii, konformno otobrazhayuschie polosu v sebya”, Sib. matem. zhurn., 21 (1980), 4–25 | MR | Zbl

[19] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974 | MR