Geodesic
On I. P. Mityuk's results on the the behavior of the inner radius of a domain and the condenser's capacity under regular mappings
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 24, Tome 371 (2009), pp. 37-55 
V. N. Dubinin. On I. P. Mityuk's results on the the behavior of the inner radius of a domain and the condenser's capacity under regular mappings. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 24, Tome 371 (2009), pp. 37-55. http://geodesic.mathdoc.fr/item/ZNSL_2009_371_a3/
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     title = {On {I.} {P.~Mityuk's} results on the the behavior of the inner radius of a~domain and the condenser's capacity under regular mappings},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The classical Lindelöf principle on the behavior of Green's function under a regular mapping is generalized to the case of Robinson's function with a pole at a boundary point. In addition reverse inequalities in the Lindelöf principle are considered. As corollaries, certain analogs of Mityuk's theorems on the behavior of the inner radius of a domain are established. Also we supplement a special case of a Mityuk's theorems and a Kloke's result on the change of the condenser capacity under a multivalent mapping. Bibl. – 19 titles.

[1] I. P. Mityuk, “Printsip simmetrizatsii dlya mnogosvyaznykh oblastei”, Dokl. AN SSSR, 157:2 (1964), 268–270 | Zbl

[2] I. P. Mityuk, “Printsip simmetrizatsii dlya mnogosvyaznykh oblastei i nekotorye ego primeneniya”, Ukr. mat. zhurn., 17:4 (1965), 46–54 | MR | Zbl

[3] I. P. Mityuk, Simmetrizatsionnye metody i ikh primenenie v geometricheskoi teorii funktsii. Vvedenie v simmetrizatsionnye metody, Izd-vo Kubanskogo un-ta, Krasnodar, 1980

[4] I. P. Mityuk, Primenenie simmetrizatsionnykh metodov v geometricheskoi teorii funktsii, Izd-vo Kubanskogo un-ta, Krasnodar, 1985

[5] I. P. Mityuk, “Otsenki vnutrennego radiusa (emkosti) nekotoroi oblasti (kondensatora)”, Izv. Sev. Kavkaz. nauchn. tsentra vyssh. shk. Estestvennye nauki, 1983, no. 3, 36–38 | MR | Zbl

[6] I. P. Mityuk, “Nekotorye svoistva funktsii, regulyarnykh v mnogosvyaznykh oblastyakh”, Dokl. AN SSSR, 164:3 (1965), 495–498 | Zbl

[7] P. Duren, “Robin capacity”, Computational methods and function theory (Nicosia, 1997), Ser. Approx. Decompos., 11, World Sci. Publ., River Edge, NJ, 1999, 177–190 | MR | Zbl

[8] V. N. Dubinin, “Obobschennye kondensatory i asimptotika ikh emkostei pri vyrozhdenii nekotorykh plastin”, Zap. nauchn. semin. POMI, 302, 2003, 38–51 | MR

[9] H. Kloke, “Some inequalities for the capacity of plane condensers”, Results Math., 9:1–2 (1986), 82–94 | DOI | MR | Zbl

[10] V. N. Dubinin, M. Vuorinen, Robin functions and distortion theorems for regular mappings, Preprint No 454, Rep. Math., Dep. Math. Stat., Univ. Helsinki, 2007 | MR

[11] V. N. Dubinin, E. G. Prilepkina, “O variatsionnykh printsipakh konformnykh otobrazhenii”, Algebra i analiz, 18:3 (2006), 39–62 | MR | Zbl

[12] P. Henrici, Applied and computational complex analysis, vol. 3, John Wiley Sons Inc., New York, 1986 | MR | Zbl

[13] A. Yu. Solynin, “Moduli i ekstremalno-metricheskie problemy”, Algebra i analiz, 11:1 (1999), 3–86 | MR | Zbl

[14] S. Stoilov, Teoriya funktsii kompleksnogo peremennogo, tom 2, M., 1962

[15] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, M., 1966 | Zbl

[16] M. H. Protter, H. F. Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984 | MR | Zbl

[17] V. N. Dubinin, “O printsipakh mazhoratsii dlya meromorfnykh funktsii”, Mat. zametki, 84:6 (2008), 803–808 | DOI | MR | Zbl

[18] J. Krzyz, “Circular symmetrization and Green's function”, Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. et Phys., 7:6 (1959), 327–330 | MR | Zbl

[19] V. N. Dubinin, “Simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo”, Uspekhi mat. nauk, 49:1 (1994), 3–76 | MR | Zbl