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This article is cited in 86 scientific papers (total in 86 papers)
Symmetrization in the geometric theory of functions of a complex variable
V. N. Dubinin Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
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Russian Mathematical Surveys, 1994, 49:1, 1–79
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UDC:
517.5
MSC: 30C85, 32A25 Received: 28.12.1992
Citation:
V. N. Dubinin, “Symmetrization in the geometric theory of functions of a complex variable”, Uspekhi Mat. Nauk, 49:1(295) (1994), 3–76; Russian Math. Surveys, 49:1 (1994), 1–79
Citation in format AMSBIB
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\jour Russian Math. Surveys
\yr 1994
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A. Yu. Solynin, “Harmonic measure of radial line segments and symmetrization”, Sb. Math., 189:11 (1998), 1701–1718
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E. G. Akhmedzyanova, V. N. Dubinin, “Radial transformations of sets, and inequalities for the transfinite diameter”, Russian Math. (Iz. VUZ), 43:4 (1999), 1–6
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L. V. Kovalev, “On the inner radii of symmetric nonoverlapping domains”, Russian Math. (Iz. VUZ), 44:6 (2000), 77–78
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L. V. Kovalev, “O trekh neperesekayuschikhsya oblastyakh”, Dalnevost. matem. zhurn., 1:1 (2000), 3–7
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V. N. Dubinin, V. Yu. Kim, “Averaging transformation of sets and functions on Riemann surfaces”, Russian Math. (Iz. VUZ), 45:5 (2001), 19–27
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E. V. Kostyuchenko, “Reshenie odnoi zadachi ob ekstremalnom razbienii”, Dalnevost. matem. zhurn., 2:1 (2001), 3–15
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Betsakos D., “Geometric Theorems and Problems for Harmonic Measure”, Rocky Mt. J. Math., 31:3 (2001), 773–795
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Dimitrios Betsakos, “Hitting probabilities of conditional Brownian motion and polarisation”, BAZ, 66:2 (2002), 233
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Christian Pommerenke, Alexander Vasil’ev, “Angular derivatives of bounded univalent functions and extremal partitions of the unit disk”, Pacific J Math, 206:2 (2002), 425
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V. N. Dubinin, E. G. Prilepkina, “K teoremam edinstvennosti dlya preobrazovanii mnozhestv i kondensatorov na ploskosti”, Dalnevost. matem. zhurn., 3:2 (2002), 137–149
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V. N. Dubinin, N. V. Eirikh, “Obobschennyi privedennyi modul”, Dalnevost. matem. zhurn., 3:2 (2002), 150–164
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V. N. Dubinin, “Generalized condensers and the asymptotics of their capacities under degeneration of some plates”, J. Math. Sci. (N. Y.), 129:3 (2005), 3835–3842
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G. V. Kuz'mina, “The method of extremal metric in extremal decomposition problems with free parameters”, J. Math. Sci. (N. Y.), 129:3 (2005), 3843–3851
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Roger W. Barnard, Kent Pearce, Alexander Yu. Solynin, “Area, width, and logarithmic capacity
of convex sets”, Pacific J Math, 212:1 (2003), 13
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N. V. Eirikh, “O privedennom module I. P. Mityuka”, Dalnevost. matem. zhurn., 4:2 (2003), 167–181
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V. N. Dubinin, N. V. Eyrikh, “Some applications of generalized condensers to analytic function theory”, J. Math. Sci. (N. Y.), 133:6 (2006), 1634–1647
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G. V. Kuz'mina, “Problems of extremal decomposition of the Riemann sphere. III”, J. Math. Sci. (N. Y.), 133:6 (2006), 1676–1685
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E. V. Kostyuchenko, E. G. Prilepkina, “O polyarizatsii otnositelno gipersfery”, Dalnevost. matem. zhurn., 5:1 (2004), 22–29
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V. N. Dubinin, E. G. Prilepkina, “O sokhranenii obobschennogo privedennogo modulya pri geometricheskikh preobrazovaniyakh ploskikh oblastei”, Dalnevost. matem. zhurn., 6:1-2 (2005), 39–56
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V. V. Aseev, A. V. Sychev, “Zapolnenie kondensatorov i skhodimost k yadru”, Vestn. NGU. Ser. matem., mekh., inform., 5:3 (2005), 3–19
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G. V. Kuz'mina, “On the occasion of the 100th anniversary of G. M. Goluzin's birthday”, J. Math. Sci. (N. Y.), 143:3 (2007), 3011–3016
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V. N. Dubinin, “Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization”, J. Math. Sci. (N. Y.), 143:3 (2007), 3053–3068
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G. V. Kuz'mina, “An extremal metric approach to some problems on extremal decomposition”, J. Math. Sci. (N. Y.), 143:3 (2007), 3124–3136
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A. Yu. Solynin, “The analytic fixed point function and its properties”, J. Math. Sci. (N. Y.), 143:3 (2007), 3153–3160
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V. N. Dubinin, “Inequalities for critical values of
polynomials”, Sb. Math., 197:8 (2006), 1167–1176
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St. Petersburg Math. J., 18:1 (2007), 21–36
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G. V. Kuz'mina, “Gennadii Mikhailovich Goluzin and geometric function theory”, St. Petersburg Math. J., 18:3 (2007), 347–372
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V. N. Dubinin, E. G. Prilepkina, “On variational principles of conformal mappings”, St. Petersburg Math. J., 18:3 (2007), 373–389
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V. N. Dubinin, “Lemniscates and Inequalities for the Logarithmic Capacities of Continua”, Math. Notes, 80:1 (2006), 31–35
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V. V. Aseev, O. A. Lazareva, “On the continuity of the reduced modulus and the transfinite diameter”, Russian Math. (Iz. VUZ), 50:10 (2006), 8–16
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V. N. Dubinin, V. Yu. Kim, “Distortion theorems for bounded regular functions in the disk”, J. Math. Sci. (N. Y.), 150:3 (2008), 2018–2026
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G. V. Kuz'mina, “On symmetric configurations in some problems on extremal decomposition”, J. Math. Sci. (N. Y.), 150:3 (2008), 2096–2104
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V. V. Aseev, “Obobschennyi privedennyi modul v prostranstvennykh zadachakh emkostnoi tomografii”, Dalnevost. matem. zhurn., 7:1-2 (2007), 17–29
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V. N. Dubinin, V. Yu. Kim, “O pokrytii radialnykh otrezkov pri $p$-listnykh otobrazheniyakh kruga i koltsa”, Dalnevost. matem. zhurn., 7:1-2 (2007), 40–47
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Solynin A.Yu., “Hyperbolic Convexity and the Analytic Fixed Point Function”, Proc. Amer. Math. Soc., 135:4 (2007), 1181–1186
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O. A. Lazareva, “Some properties of the reduced modulus in space”, Siberian Math. J., 49:1 (2008), 117–122
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A. K. Bakhtin, “Inequalities for Inner Radii of Disjoint Domains and Open Sets”, Proc. Steklov Inst. Math., 261 (2008), 34–43
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V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, J. Math. Sci. (N. Y.), 157:4 (2009), 573–583
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G. V. Kuz'mina, “On symmetric configurations in some problems on extremal decomposition. II”, J. Math. Sci. (N. Y.), 157:4 (2009), 632–645
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V. N. Dubinin, D. B. Karp, V. A. Shlyk, “Izbrannye zadachi geometricheskoi teorii funktsii i teorii potentsiala”, Dalnevost. matem. zhurn., 8:1 (2008), 46–95
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V. N. Dubinin, “Emkosti kondensatorov i printsipy mazhoratsii v geometricheskoi teorii funktsii kompleksnogo peremennogo [Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke”]”, Sib. elektron. matem. izv., 5 (2008), 465–482
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V. N. Dubinin, D. Karp, “Capacities of certain plane condensers and sets under simple geometric transformations”, Complex Variables and Elliptic Equations, 53:6 (2008), 607
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V. N. Dubinin, M. Vuorinen, “On conformal moduli of polygonal quadrilaterals”, Isr J Math, 171:1 (2009), 111
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V. V. Aseev, “Ned sets on a hyperplane”, Siberian Math. J., 50:5 (2009), 760–775
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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”, J. Math. Sci. (N. Y.), 166:2 (2010), 145–154
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V. N. Dubinin, “Emkosti kondensatorov i simmetrizatsiya v zadachakh ob ekstremalnom razbienii”, Dalnevost. matem. zhurn., 9:1-2 (2009), 84–93
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V. N. Dubinin, E. G. Prilepkina, “Distortion theorems for univalent meromorphic functions on an annulus”, Siberian Math. J., 51:2 (2010), 229–243
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V. V. Aseev, “Convex expansion of condenser plates”, Russian Math. (Iz. VUZ), 54:8 (2010), 1–11
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D. A. Kirillova, “Univalent functions without common values”, Russian Math. (Iz. VUZ), 54:9 (2010), 74–76
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V. N. Dubinin, “Steiner symmetrization and the initial coefficients of univalent functions”, Izv. Math., 74:4 (2010), 735–742
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D. A. Kirillova, “O maksimume mebiusova invarianta v zadache s chetyrmya nenalegayuschimi oblastyami”, Dalnevost. matem. zhurn., 10:1 (2010), 41–49
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V. N. Dubinin, D. A. Kirillova, “Nekotorye primeneniya ekstremalnykh razbienii v geometricheskoi teorii funktsii”, Dalnevost. matem. zhurn., 10:2 (2010), 130–152
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V. N. Dubinin, “On the Finite-Increment Theorem for Complex Polynomials”, Math. Notes, 88:5 (2010), 647–654
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V. N. Dubinin, “Geometric versions of Schwarz lemma and symmetrization”, J. Math. Sci. (N. Y.), 178:2 (2011), 150–157
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V. N. Dubinin, “On the components of the lemniscate containing no critical points of a polynomial other than its zeros”, J. Math. Sci. (N. Y.), 178:2 (2011), 158–162
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G. V. Kuz'mina, “The method of extremal metric in the problem on the maximum of a conformal invariant”, J. Math. Sci. (N. Y.), 178:2 (2011), 187–197
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V. N. Dubinin, “Lower bounds for the half-plane capacity of compact sets and symmetrization”, Sb. Math., 201:11 (2010), 1635–1646
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V. N. Dubinin, D. Karp, “Two-sided bounds for the logarithmic capacity of multiple intervals”, Jama, 113:1 (2011), 227
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V. N. Dubinin, “Boundary values of the Schwarzian derivative of a regular function”, Sb. Math., 202:5 (2011), 649–663
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A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, “Variation of the equilibrium energy and the $S$-property of stationary compact sets”, Sb. Math., 202:12 (2011), 1831–1852
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A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131
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V. N. Dubinin, “On the preservation of conformal capacity under meromorphic functions”, J. Math. Sci. (N. Y.), 184:6 (2012), 699–702
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G. V. Kuz'mina, “Problems on the maximum of a conformal invariant in the presence of a high degree of symmetry”, J. Math. Sci. (N. Y.), 184:6 (2012), 746–752
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S. P. Suetin, “An analogue of the Hadamard and Schiffer variational formulas”, Theoret. and Math. Phys., 170:3 (2012), 274–279
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V. N. Dubinin, “A new version of circular symmetrization with applications to $p$-valent functions”, Sb. Math., 203:7 (2012), 996–1011
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St. Petersburg Math. J., 24:1 (2013), 117–166
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V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684
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J. Math. Sci. (N. Y.), 193:1 (2013), 66–74
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G. V. Kuz'mina, “Quadratic differentials with strip domains in the structure of trajectories in some extremal decomposition problems”, J. Math. Sci. (N. Y.), 193:1 (2013), 115–123
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V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Method of interior variations and existence of $S$-compact sets”, Proc. Steklov Inst. Math., 279 (2012), 25–51
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A. Yu. Vasiliev, A. G. Sergeev, “Classical and quantum Teichmüller spaces”, Russian Math. Surveys, 68:3 (2013), 435–502
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Walter Bergweiler, Alexandre Eremenko, “Gol’dberg’s constants”, JAMA, 119:1 (2013), 365
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V. N. Dubinin, “On the Jenkins covering circle theorem for holomorphic functions in a disk”, J. Math. Sci. (N. Y.), 200:5 (2014), 551–558
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V. O. Kuznetsov, “Some geometrical properties of extremal decompositions”, J. Math. Sci. (N. Y.), 200:5 (2014), 586–594
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S. Yu. Graf, “Teoremy rosta v klassakh normirovannykh lokalno-kvazikonformnykh otobrazhenii”, Probl. anal. Issues Anal., 2(20):2 (2013), 3–20
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Dimitrios Betsakos, “Lindelöf’s Principle and Estimates for Holomorphic Functions Involving Area, Diameter or Integral Means”, Comput. Methods Funct. Theory, 2014
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V. N. Dubinin, “Asymptotic Behavior of the Capacity of a Condenser as Some of Its Plates Contract to Points”, Math. Notes, 96:2 (2014), 187–198
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Dubinin V.N., Vuorinen M., “Ahlfors-Beurling Conformal Invariant and Relative Capacity of Compact Sets”, Proc. Amer. Math. Soc., 142:11 (2014), 3865–3879
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V. N. Dubinin, “Circular symmetrization of condensers on Riemann surfaces”, Sb. Math., 206:1 (2015), 61–86
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Riku Klén, Matti Vuorinen, Xiaohui Zhang, “On Isometries of Conformally Invariant Metrics”, J Geom Anal, 2015
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Galatia Cleanthous, A.G.. Georgiadis, “Upper and Lower Estimates for the Modulus of Bounded Holomorphic Functions”, Complex Anal. Oper. Theory, 2015
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V. O. Kuznetsov, “Polarization and circular truncation of a domain”, J. Math. Sci. (N. Y.), 217:1 (2016), 108–113
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V. O. Kuznetsov, “Inner radius, polarization and circular truncation of the set”, J. Math. Sci. (N. Y.), 222:5 (2017), 641–644
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J. Math. Sci. (N. Y.), 222:5 (2017), 645–689
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G. V. Kuz'mina, “On an extremal metric approach to extremal decomposition problems”, J. Math. Sci. (N. Y.), 225:6 (2017), 980–990
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Dubinin V.N., “Some Unsolved Problems About Condenser Capacities on the Plane”, Complex Analysis and Dynamical Systems: New Trends and Open Problems, Trends in Mathematics, ed. Agranovsky M. Golberg A. Jacobzon F. Shoikhet D. Zalcman L., Birkhauser Verlag Ag, 2018, 81–92
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