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

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Uspekhi Mat. Nauk, 1994, Volume 49, Issue 1(295), Pages 3–76 (Mi umn1153)

This article is cited in 88 scientific papers (total in 88 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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English version:
Russian Mathematical Surveys, 1994, 49:1, 1–79

Bibliographic databases:

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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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:

A. Yu. Solynin, “Harmonic measure of radial line segments and symmetrization”, Sb. Math., 189:11 (1998), 1701–1718
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
L. V. Kovalev, “On the inner radii of symmetric nonoverlapping domains”, Russian Math. (Iz. VUZ), 44:6 (2000), 77–78
L. V. Kovalev, “O trekh neperesekayuschikhsya oblastyakh”, Dalnevost. matem. zhurn., 1:1 (2000), 3–7
V. N. Dubinin, V. Yu. Kim, “Averaging transformation of sets and functions on Riemann surfaces”, Russian Math. (Iz. VUZ), 45:5 (2001), 19–27
E. V. Kostyuchenko, “Reshenie odnoi zadachi ob ekstremalnom razbienii”, Dalnevost. matem. zhurn., 2:1 (2001), 3–15
Betsakos D., “Geometric Theorems and Problems for Harmonic Measure”, Rocky Mt. J. Math., 31:3 (2001), 773–795
Dimitrios Betsakos, “Hitting probabilities of conditional Brownian motion and polarisation”, BAZ, 66:2 (2002), 233
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
V. N. Dubinin, E. G. Prilepkina, “K teoremam edinstvennosti dlya preobrazovanii mnozhestv i kondensatorov na ploskosti”, Dalnevost. matem. zhurn., 3:2 (2002), 137–149
V. N. Dubinin, N. V. Eirikh, “Obobschennyi privedennyi modul”, Dalnevost. matem. zhurn., 3:2 (2002), 150–164
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
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
Roger W. Barnard, Kent Pearce, Alexander Yu. Solynin, “Area, width, and logarithmic capacity of convex sets”, Pacific J Math, 212:1 (2003), 13
N. V. Eirikh, “O privedennom module I. P. Mityuka”, Dalnevost. matem. zhurn., 4:2 (2003), 167–181
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
G. V. Kuz'mina, “Problems of extremal decomposition of the Riemann sphere. III”, J. Math. Sci. (N. Y.), 133:6 (2006), 1676–1685
E. V. Kostyuchenko, E. G. Prilepkina, “O polyarizatsii otnositelno gipersfery”, Dalnevost. matem. zhurn., 5:1 (2004), 22–29
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
V. V. Aseev, A. V. Sychev, “Zapolnenie kondensatorov i skhodimost k yadru”, Vestn. NGU. Ser. matem., mekh., inform., 5:3 (2005), 3–19
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
V. N. Dubinin, “Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization”, J. Math. Sci. (N. Y.), 143:3 (2007), 3053–3068
G. V. Kuz'mina, “An extremal metric approach to some problems on extremal decomposition”, J. Math. Sci. (N. Y.), 143:3 (2007), 3124–3136
A. Yu. Solynin, “The analytic fixed point function and its properties”, J. Math. Sci. (N. Y.), 143:3 (2007), 3153–3160
V. N. Dubinin, “Inequalities for critical values of polynomials”, Sb. Math., 197:8 (2006), 1167–1176
St. Petersburg Math. J., 18:1 (2007), 21–36
G. V. Kuz'mina, “Gennadii Mikhailovich Goluzin and geometric function theory”, St. Petersburg Math. J., 18:3 (2007), 347–372
V. N. Dubinin, E. G. Prilepkina, “On variational principles of conformal mappings”, St. Petersburg Math. J., 18:3 (2007), 373–389
V. N. Dubinin, “Lemniscates and Inequalities for the Logarithmic Capacities of Continua”, Math. Notes, 80:1 (2006), 31–35
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
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
G. V. Kuz'mina, “On symmetric configurations in some problems on extremal decomposition”, J. Math. Sci. (N. Y.), 150:3 (2008), 2096–2104
V. V. Aseev, “Obobschennyi privedennyi modul v prostranstvennykh zadachakh emkostnoi tomografii”, Dalnevost. matem. zhurn., 7:1-2 (2007), 17–29
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
Solynin A.Yu., “Hyperbolic Convexity and the Analytic Fixed Point Function”, Proc. Amer. Math. Soc., 135:4 (2007), 1181–1186
O. A. Lazareva, “Some properties of the reduced modulus in space”, Siberian Math. J., 49:1 (2008), 117–122
A. K. Bakhtin, “Inequalities for Inner Radii of Disjoint Domains and Open Sets”, Proc. Steklov Inst. Math., 261 (2008), 34–43
V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, J. Math. Sci. (N. Y.), 157:4 (2009), 573–583
G. V. Kuz'mina, “On symmetric configurations in some problems on extremal decomposition. II”, J. Math. Sci. (N. Y.), 157:4 (2009), 632–645
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
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
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
V. N. Dubinin, M. Vuorinen, “On conformal moduli of polygonal quadrilaterals”, Isr J Math, 171:1 (2009), 111
V. V. Aseev, “Ned sets on a hyperplane”, Siberian Math. J., 50:5 (2009), 760–775
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
V. N. Dubinin, “Emkosti kondensatorov i simmetrizatsiya v zadachakh ob ekstremalnom razbienii”, Dalnevost. matem. zhurn., 9:1-2 (2009), 84–93
V. N. Dubinin, E. G. Prilepkina, “Distortion theorems for univalent meromorphic functions on an annulus”, Siberian Math. J., 51:2 (2010), 229–243
V. V. Aseev, “Convex expansion of condenser plates”, Russian Math. (Iz. VUZ), 54:8 (2010), 1–11
D. A. Kirillova, “Univalent functions without common values”, Russian Math. (Iz. VUZ), 54:9 (2010), 74–76
V. N. Dubinin, “Steiner symmetrization and the initial coefficients of univalent functions”, Izv. Math., 74:4 (2010), 735–742
D. A. Kirillova, “O maksimume mebiusova invarianta v zadache s chetyrmya nenalegayuschimi oblastyami”, Dalnevost. matem. zhurn., 10:1 (2010), 41–49
V. N. Dubinin, D. A. Kirillova, “Nekotorye primeneniya ekstremalnykh razbienii v geometricheskoi teorii funktsii”, Dalnevost. matem. zhurn., 10:2 (2010), 130–152
V. N. Dubinin, “On the Finite-Increment Theorem for Complex Polynomials”, Math. Notes, 88:5 (2010), 647–654
V. N. Dubinin, “Geometric versions of Schwarz lemma and symmetrization”, J. Math. Sci. (N. Y.), 178:2 (2011), 150–157
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
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
V. N. Dubinin, “Lower bounds for the half-plane capacity of compact sets and symmetrization”, Sb. Math., 201:11 (2010), 1635–1646
V. N. Dubinin, D. Karp, “Two-sided bounds for the logarithmic capacity of multiple intervals”, Jama, 113:1 (2011), 227
V. N. Dubinin, “Boundary values of the Schwarzian derivative of a regular function”, Sb. Math., 202:5 (2011), 649–663
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
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
V. N. Dubinin, “On the preservation of conformal capacity under meromorphic functions”, J. Math. Sci. (N. Y.), 184:6 (2012), 699–702
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
S. P. Suetin, “An analogue of the Hadamard and Schiffer variational formulas”, Theoret. and Math. Phys., 170:3 (2012), 274–279
V. N. Dubinin, “A new version of circular symmetrization with applications to $p$-valent functions”, Sb. Math., 203:7 (2012), 996–1011
St. Petersburg Math. J., 24:1 (2013), 117–166
V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684
J. Math. Sci. (N. Y.), 193:1 (2013), 66–74
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
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
A. Yu. Vasiliev, A. G. Sergeev, “Classical and quantum Teichmüller spaces”, Russian Math. Surveys, 68:3 (2013), 435–502
Walter Bergweiler, Alexandre Eremenko, “Gol’dberg’s constants”, JAMA, 119:1 (2013), 365
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
V. O. Kuznetsov, “Some geometrical properties of extremal decompositions”, J. Math. Sci. (N. Y.), 200:5 (2014), 586–594
S. Yu. Graf, “Teoremy rosta v klassakh normirovannykh lokalno-kvazikonformnykh otobrazhenii”, Probl. anal. Issues Anal., 2(20):2 (2013), 3–20
Dimitrios Betsakos, “Lindelöf’s Principle and Estimates for Holomorphic Functions Involving Area, Diameter or Integral Means”, Comput. Methods Funct. Theory, 2014
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
Dubinin V.N., Vuorinen M., “Ahlfors-Beurling Conformal Invariant and Relative Capacity of Compact Sets”, Proc. Amer. Math. Soc., 142:11 (2014), 3865–3879
V. N. Dubinin, “Circular symmetrization of condensers on Riemann surfaces”, Sb. Math., 206:1 (2015), 61–86
Riku Klén, Matti Vuorinen, Xiaohui Zhang, “On Isometries of Conformally Invariant Metrics”, J Geom Anal, 2015
Galatia Cleanthous, A.G.. Georgiadis, “Upper and Lower Estimates for the Modulus of Bounded Holomorphic Functions”, Complex Anal. Oper. Theory, 2015
V. O. Kuznetsov, “Polarization and circular truncation of a domain”, J. Math. Sci. (N. Y.), 217:1 (2016), 108–113
V. O. Kuznetsov, “Inner radius, polarization and circular truncation of the set”, J. Math. Sci. (N. Y.), 222:5 (2017), 641–644
J. Math. Sci. (N. Y.), 222:5 (2017), 645–689
G. V. Kuz'mina, “On an extremal metric approach to extremal decomposition problems”, J. Math. Sci. (N. Y.), 225:6 (2017), 980–990
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
A. K. Bakhtin, I. V. Denega, “Sharp estimates of products of inner radii of non-overlapping domains in the complex plane”, Probl. anal. Issues Anal., 8(26):1 (2019), 17–31
Iryna Denega, “Estimate of the maximum product of inner radii of non-overlapping domains”, Probl. anal. Issues Anal., 9(27):1 (2020), 60–65

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