Geometric function theory, potential theory, isoperimetric inequalities in mathematical physics. General symmetrization principles for various symmetrization-like transformation of condensers in n-space have been established for a wide range of capacities induced by functionals dependent on the argument, the function and its first partial derivatives. Generalized condensers having three and more plates on the Riemann sphere have been first introduced and studied. Common properties of these condensers and asymptotic formulas for their capacities under degeneration of some plates have been found. General approach to application of conformal capacity of condensers and their symmetrization in geometric theory of functions of a complex variable has been developed. In particular, new metric properties of plane sets have been found, extremal decomposition theorems with free poles and new covering and distortion theorems for univalent and multivalent functions proved. New properties of polynomials and rational functions have been established using geometric function theory methods. In particular, new Bernstein-type inequalities and some inequalities for zeros, critical points and critical values of polynomials have been proved.
Biography
Graduated with honors as mathematics major from the Far Eastern State University in 1973 and entered postgraduate course at the chair of function theory of the Kuban State University (Krasnodar) the same year. Depended PhD (candidate of Science) thesis entitled “Certain symmetrization-like transformations and covering problems in geometric theory of functions of a complex variable” at the Applied Mathematics and Mechanics Institute of the Ukranian Academy of Sciences (Donetsk) in 1977. Scientific Advisor – professor I.P. Mityuk. Defended habilitation thesis (Doctor of Science) entitled “Symmetrization method in geometric function theory” at the Mathematics Institute of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk). Has been elected correspondent member of the Russian Academy of Sciences (Far Eastern Branch) in 2003. Teaching – 1977-78 – assistant teacher, 1978-83 – senior teacher, 1983-1989 – docent (associate professor), 1989 – present full professor of the chair of mathematical analysis at the Far Eastern State University (at present chair of function theory and functional analysis). The head of the laboratory of mathematical analysis at the Institute of Applied Mathematics of the Far Eastern Branch of the Russian Academy of Sciences since 1991.
Main publications:
Дубинин В.Н., Емкости конденсаторов и симметризация в геометрической теории функций комплексного переменного, Дальнаука, Владивосток, 2009
Дубинин В.Н., Емкости конденсаторов и симметризация в геометрической теории функций комплексного переменного, Дальнаука, 2009
V. N. Dubinin, “An Extremal Problem for the Derivative of a Rational Function”, Math. Notes, 100:5 (2016), 714–719
2.
V. N. Dubinin, “Critical values and moduli of derivative of a complex polynomial at its zeros”, Zap. Nauchn. Sem. POMI, 449, 2016, 60–68
3.
V. N. Dubinin, “The logarithmic energy of zeros and poles of a rational function”, Siberian Math. J., 57:6 (2016), 981–986
2015
4.
V. N. Dubinin, “Circular symmetrization of condensers on Riemann surfaces”, Sb. Math., 206:1 (2015), 61–86 (cited: 1) (cited: 2)
5.
V. N. Dubinin, “Schwarzian Derivative and Covering Arcs of a Pencil of Circles by Holomorphic Functions”, Math. Notes, 98:6 (2015), 920–925 (cited: 1)
6.
V. N. Dubinin, “Teoremy iskazheniya dlya funktsii, $p$-listnykh v srednem po okruzhnosti”, Analiticheskaya teoriya chisel i teoriya funktsii. 30, Zap. nauchn. sem. POMI, 440, POMI, SPb., 2015, 43–56; V. N. Dubinin, “Distortion theorems for circumferentially mean $p$-valent functions”, J. Math. Sci. (N. Y.), 217:1 (2016), 28–36
7.
V. N. Dubinin, “Inequalities for harmonic measures with respect to non-overlapping domains”, Izv. Math., 79:5 (2015), 902–918 (cited: 1)
8.
V. M. Buchstaber, V. N. Dubinin, V. A. Kaliaguine, B. S. Kashin, V. N. Sorokin, S. P. Suetin, D. N. Tulyakov, B. N. Chetverushkin, E. M. Chirka, A. A. Shkalikov, “Alexander Ivanovich Aptekarev (on his 60th birthday)”, Russian Math. Surveys, 70:5 (2015), 965–973
2014
9.
V. N. Dubinin, “Two-point boundary distortion estimate for Schwarzian derivative of holomorphic function”, FEMJ, 14:2 (2014), 191–199
10.
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 (cited: 1) (cited: 1) (cited: 1) (cited: 1)
11.
V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892 (cited: 1) (cited: 1) (cited: 1) (cited: 1)
12.
V. N. Dubinin, “On one extremal problem for complex polynomials with constraints on critical values”, Siberian Math. J., 55:1 (2014), 63–71 (cited: 1)
13.
V. N. Dubinin, “Neravenstva dlya modulei funktsii, $p$-listnykh v srednem po okruzhnosti”, Analiticheskaya teoriya chisel i teoriya funktsii. 29, Zap. nauchn. sem. POMI, 429, POMI, SPb., 2014, 44–54 (cited: 1); V. N. Dubinin, “Inequalities for moduli of the circumferentially mean $p$-valent functions”, J. Math. Sci. (N. Y.), 207:6 (2015), 832–838
14.
V. N. Dubinin, “Golomorfnye ogranichennye funktsii, ne pokryvayuschie kontsentricheskikh okruzhnostei”, Analiticheskaya teoriya chisel i teoriya funktsii. 29, Zap. nauchn. sem. POMI, 429, POMI, SPb., 2014, 34–43 (cited: 1); V. N. Dubinin, “Bounded holomorphic functions covering no concentric circles”, J. Math. Sci. (N. Y.), 207:6 (2015), 825–831 (cited: 2)
15.
F. G. Avkhadiev, V. A. Botvinnik, S. K. Vodop'yanov, M. Vuorinen, V. M. Gol'dstein, V. V. Goryainov, A. A. Grigor'yan, V. N. Dubinin, I. V. Zhuravlev, V. A. Zorich, V. M. Kesel'man, V. A. Klyachin, T. G. Latfullin, A. V. Loboda, A. G. Losev, O. Martio, V. I. Pelikh, S. I. Pinchuk, Yu. G. Reshetnyak, A. S. Romanov, A. G. Sergeev, V. G. Tkachev, E. M. Chirka, “Vladimir Mikhailovich Miklyukov (obituary)”, Russian Math. Surveys, 69:3 (2014), 565–568
2013
16.
V. N. Dubinin, V. Yu. Kim, “Generalized condensers and boundary distortion theorems for conformal mappings”, FEMJ, 13:2 (2013), 196–208
17.
V. N. Dubinin, “Symmetrization of Condensers and Inequalities for Functions Multivalent in a Disk”, Math. Notes, 94:6 (2013), 876–884 (cited: 1) (cited: 2) (cited: 2) (cited: 2)
18.
V. N. Dubinin, “K teoreme Dzhenkinsa o pokrytii okruzhnostei golomorfnymi v kruge funktsiyami”, Analiticheskaya teoriya chisel i teoriya funktsii. 28, Zap. nauchn. sem. POMI, 418, POMI, SPb., 2013, 60–73 (cited: 3); 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
2012
19.
V. N. Dubinin, “On a Class of Univalent Functions”, FEMJ, 12:2 (2012), 184–194
20.
V. N. Dubinin, “Ekstremalnye zadachi Gretsha i Teikhmyullera na rimanovoi poverkhnosti”, Matem. zametki, 92:6 (2012), 834–843 (cited: 4) (cited: 2); V. N. Dubinin, “The Grötzsch and Teichmüller Extremal Problems on a Riemann Surface”, Math. Notes, 93:1 (2013), 50–57 (cited: 2) (cited: 2) (cited: 1)
21.
V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684 (cited: 5) (cited: 5) (cited: 5) (cited: 5)
22.
V. N. Dubinin, “A new version of circular symmetrization with applications to $p$-valent functions”, Sb. Math., 203:7 (2012), 996–1011 (cited: 5) (cited: 7) (cited: 7) (cited: 6)
23.
V. N. Dubinin, “Nekotorye neravenstva dlya polinomov i ratsionalnykh funktsii, svyazannye s lemniskatami”, Analiticheskaya teoriya chisel i teoriya funktsii. 27, Zap. nauchn. sem. POMI, 404, POMI, SPb., 2012, 83–99 (cited: 1); V. N. Dubinin, “Some inequalities for polynomials and rational functions associated with a lemniscate”, J. Math. Sci. (N. Y.), 193:1 (2013), 45–54 (cited: 1)
2011
24.
V. N. Dubinin, “On the distortion theorems for algebraic polynomials”, FEMJ, 11:1 (2011), 28–36
25.
V. N. Dubinin, “Lower Bound for the Discrete Norm of a Polynomial on the Circle”, Math. Notes, 90:2 (2011), 284–287 (cited: 3) (cited: 2) (cited: 2) (cited: 3)
26.
V. N. Dubinin, “Boundary values of the Schwarzian derivative of a regular function”, Sb. Math., 202:5 (2011), 649–663 (cited: 3) (cited: 2) (cited: 2) (cited: 2)
27.
V. N. Dubinin, S. I. Kalmykov, “O polinomakh s ogranicheniyami na dugakh okruzhnosti”, Analiticheskaya teoriya chisel i teoriya funktsii. 26, Zap. nauchn. sem. POMI, 392, POMI, SPb., 2011, 74–83 (cited: 3); V. N. Dubinin, S. I. Kalmukov, “On polynomials with constraints on circular arcs”, J. Math. Sci. (N. Y.), 184:6 (2012), 703–708 (cited: 1)
28.
V. N. Dubinin, “O sokhranenii konformnoi emkosti pri otobrazhenii meromorfnymi funktsiyami”, Analiticheskaya teoriya chisel i teoriya funktsii. 26, Zap. nauchn. sem. POMI, 392, POMI, SPb., 2011, 67–73 (cited: 2); V. N. Dubinin, “On the preservation of conformal capacity under meromorphic functions”, J. Math. Sci. (N. Y.), 184:6 (2012), 699–702 (cited: 2)
2010
29.
V. N. Dubinin, D. A. Kirillova, “Some applications of extremal decompositions in the geometric function theory”, FEMJ, 10:2 (2010), 130–152
30.
V. N. Dubinin, “Steiner symmetrization and the initial coefficients of univalent functions”, Izv. Math., 74:4 (2010), 735–742 (cited: 2) (cited: 1) (cited: 1)
31.
V. N. Dubinin, “On the Finite-Increment Theorem for Complex Polynomials”, Math. Notes, 88:5 (2010), 647–654 (cited: 1) (cited: 2) (cited: 2) (cited: 2)
32.
V. N. Dubinin, “Lower bounds for the half-plane capacity of compact sets and symmetrization”, Sb. Math., 201:11 (2010), 1635–1646 (cited: 2) (cited: 1) (cited: 1) (cited: 1)
33.
V. N. Dubinin, E. G. Prilepkina, “Distortion theorems for univalent meromorphic functions on an annulus”, Siberian Math. J., 51:2 (2010), 229–243
34.
V. N. Dubinin, “O komponentakh lemniskaty, ne soderzhaschikh kriticheskikh tochek polinoma, otlichnykh ot ego nulei”, Analiticheskaya teoriya chisel i teoriya funktsii. 25, Zap. nauchn. sem. POMI, 383, POMI, SPb., 2010, 77–85 (cited: 1); 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 (cited: 1)
35.
V. N. Dubinin, “Geometricheskie versii lemmy Shvartsa i simmetrizatsiya”, Analiticheskaya teoriya chisel i teoriya funktsii. 25, Zap. nauchn. sem. POMI, 383, POMI, SPb., 2010, 63–76 (cited: 3); V. N. Dubinin, “Geometric versions of Schwarz lemma and symmetrization”, J. Math. Sci. (N. Y.), 178:2 (2011), 150–157 (cited: 5)
2009
36.
V. N. Dubinin, “Condenser capacity and symmetrization in the extremal decomposition problems”, FEMJ, 9:1-2 (2009), 84–93
37.
V. N. Dubinin, “Quadratic forms involving Green's and Robin functions”, Sb. Math., 200:10 (2009), 1439–1452 (cited: 3) (cited: 2) (cited: 2) (cited: 2)
38.
V. N. Dubinin, “K rezultatam I. P. Mityuka o povedenii vnutrennego radiusa oblasti i emkosti kondensatora pri regulyarnykh otobrazheniyakh”, Analiticheskaya teoriya chisel i teoriya funktsii. 24, Zap. nauchn. sem. POMI, 371, POMI, SPb., 2009, 37–55 (cited: 1); 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
39.
V. N. Dubinin, G. V. Kuz'mina, “Igor Petrovich Mityuk (1928–1995). On the occasion of the 80 anniversary of birthday”, Analytical theory of numbers and theory of functions. Part 24, Zap. Nauchn. Sem. POMI, 371, POMI, St. Petersburg, 2009, 5
2008
40.
V. N. Dubinin, D. B. Karp, V. A. Shlyk, “Selected problems of geometrical theory of functions and potential theory”, FEMJ, 8:1 (2008), 46–95
41.
V. N. Dubinin, “Majorization Principles for Meromorphic Functions”, Math. Notes, 84:6 (2008), 751–755 (cited: 3) (cited: 3) (cited: 3) (cited: 2)
42.
V. N. Dubinin, “Condenser capacities and majorization principles in the geometric function theory of a complex variable”, Sib. Èlektron. Mat. Izv., 5 (2008), 465–482
43.
V. V. Vasin, V. N. Dubinin, V. G. Romanov, “Concluding scientific report for the project of Siberian Division of RAS: “A development of theory and computational technology for solving inverse and extremal problems with an application to mathematical physics and gravity-magneto-prospecting””, Sib. Èlektron. Mat. Izv., 5 (2008), 427–439
44.
V. N. Dubinin, D. A. Kirillova, “K zadacham ob ekstremalnom razbienii”, Analiticheskaya teoriya chisel i teoriya funktsii. 23, Zap. nauchn. sem. POMI, 357, POMI, SPb., 2008, 54–74 (cited: 7) ; V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, J. Math. Sci. (N. Y.), 157:4 (2009), 573–583
2007
45.
V. N. Dubinin, V. Yu. Kim, “On the covering of radial segments under $p$-valent mappings of a disk and an annulus”, FEMJ, 7:1-2 (2007), 40–47
46.
V. N. Dubinin, S. I. Kalmykov, “A majoration principle for meromorphic functions”, Sb. Math., 198:12 (2007), 1737–1745 (cited: 3) (cited: 6) (cited: 6) (cited: 2)
47.
V. N. Dubinin, V. Yu. Kim, “Teoremy iskazheniya dlya regulyarnykh i ogranichennykh v kruge funktsii”, Analiticheskaya teoriya chisel i teoriya funktsii. 22, Zap. nauchn. sem. POMI, 350, POMI, SPb., 2007, 26–39 (cited: 6) (cited: 1); 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 (cited: 1) (cited: 2)
2006
48.
V. N. Dubinin, E. G. Prilepkina, “O variatsionnykh printsipakh konformnykh otobrazhenii”, Algebra i analiz, 18:3 (2006), 39–62 (cited: 6) (cited: 3) (cited: 3); V. N. Dubinin, E. G. Prilepkina, “On variational principles of conformal mappings”, St. Petersburg Math. J., 18:3 (2007), 373–389
49.
V. N. Dubinin, “Lemniscates and Inequalities for the Logarithmic Capacities of Continua”, Math. Notes, 80:1 (2006), 31–35 (cited: 1) (cited: 1) (cited: 1) (cited: 1)
50.
V. N. Dubinin, “Inequalities for critical values of polynomials”, Sb. Math., 197:8 (2006), 1167–1176 (cited: 4) (cited: 8) (cited: 8) (cited: 6)
51.
V. N. Dubinin, “O primenenii lemmy Shvartsa k neravenstvam dlya tselykh funktsii s ogranicheniyami na nuli”, Analiticheskaya teoriya chisel i teoriya funktsii. 21, Zap. nauchn. sem. POMI, 337, POMI, SPb., 2006, 101–112 (cited: 7) (cited: 2) (cited: 4); V. N. Dubinin, “Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros”, J. Math. Sci. (N. Y.), 143:3 (2007), 3069–3076 (cited: 3) (cited: 3)
52.
V. N. Dubinin, “Emkosti kondensatorov, obobscheniya lemm Grëtsha i simmetrizatsiya”, Analiticheskaya teoriya chisel i teoriya funktsii. 21, Zap. nauchn. sem. POMI, 337, POMI, SPb., 2006, 73–100 (cited: 9) (cited: 4) (cited: 4); V. N. Dubinin, “Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization”, J. Math. Sci. (N. Y.), 143:3 (2007), 3053–3068
2005
53.
V. N. Dubinin, E. G. Prilepkina, “On the preservation of generalized reduced modulus under some geometric transformations of domains in the plane”, FEMJ, 6:1-2 (2005), 39–56
54.
V. N. Dubinin, “Polynomials with Critical Values on Intervals”, Math. Notes, 78:6 (2005), 768–772 (cited: 1) (cited: 1) (cited: 1) (cited: 1)
55.
V. N. Dubinin, “Schwarz's lemma and estimates of coefficients for regular functions with free domain of definition”, Sb. Math., 196:11 (2005), 1605–1625 (cited: 3) (cited: 2) (cited: 2) (cited: 3)
2004
56.
V. N. Dubinin, S. I. Kalmykov, “Extremal properties of Chebyshev polynomials”, FEMJ, 5:2 (2004), 169–177
57.
V. N. Dubinin, N. V. Eirikh, “Nekotorye primeneniya obobschennykh kondensatorov v teorii analiticheskikh funktsii”, Analiticheskaya teoriya chisel i teoriya funktsii. 20, Zap. nauchn. sem. POMI, 314, POMI, SPb., 2004, 52–75 (cited: 13) (cited: 9) (cited: 15); 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 (cited: 5)
2003
58.
V. N. Dubinin, “Obobschennye kondensatory i asimptotika ikh ëmkostei pri vyrozhdenii nekotorykh plastin”, Analiticheskaya teoriya chisel i teoriya funktsii. 19, Zap. nauchn. sem. POMI, 302, POMI, SPb., 2003, 38–51 (cited: 22) (cited: 18) ; 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
59.
V. N. Dubinin, “Konformnye otobrazheniya i neravenstva dlya algebraicheskikh polinomov. II”, Analiticheskaya teoriya chisel i teoriya funktsii. 19, Zap. nauchn. sem. POMI, 302, POMI, SPb., 2003, 18–37 (cited: 5) (cited: 2) ; V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials. II”, J. Math. Sci. (N. Y.), 129:3 (2005), 3823–3834
2002
60.
V. N. Dubinin, N. V. Eyrikh, “The generalized reduced modulus”, FEMJ, 3:2 (2002), 150–164
61.
V. N. Dubinin, E. G. Prilepkina, “On the uniqueness theorems for the transformations of sets and condensers in the plane”, FEMJ, 3:2 (2002), 137–149
62.
V. N. Dubinin, “On an application of conformal maps to inequalities for rational functions”, Izv. Math., 66:2 (2002), 285–297 (cited: 1)
63.
V. N. Dubinin, A. V. Olesov, “O primenenii konformnykh otobrazhenii k neravenstam dlya polinomov”, Analiticheskaya teoriya chisel i teoriya funktsii. 18, Zap. nauchn. sem. POMI, 286, POMI, SPb., 2002, 85–102 (cited: 6) (cited: 2) ; V. N. Dubinin, A. V. Olesov, “Application of conformal mappings to the inequalities for polynomials”, J. Math. Sci. (N. Y.), 122:6 (2004), 3630–3640
64.
V. N. Dubinin, “K neravenstvu Shvartsa na granitse dlya regulyarnykh v kruge funktsii”, Analiticheskaya teoriya chisel i teoriya funktsii. 18, Zap. nauchn. sem. POMI, 286, POMI, SPb., 2002, 74–84 (cited: 11) (cited: 11) ; V. N. Dubinin, “On the Shwarz inequality on the boundary for functions regular in the disk”, J. Math. Sci. (N. Y.), 122:6 (2004), 3623–3629
2001
65.
V. N. Dubinin, “Konformnye otobrazheniya i neravenstva dlya algebraicheskikh polinomov”, Algebra i analiz, 13:5 (2001), 16–43 (cited: 26) (cited: 21) ; V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials”, St. Petersburg Math. J., 13:5 (2002), 717–737
66.
V. N. Dubinin, V. Yu. Kim, “Averaging transformation of sets and functions on Riemann surfaces”, Russian Math. (Iz. VUZ), 45:5 (2001), 19–27
67.
V. N. Dubinin, E. V. Kostyuchenko, “Ekstremalnye zadachi teorii funktsii, svyazannye s $n$-kratnoi simmetriei”, Analiticheskaya teoriya chisel i teoriya funktsii. 17, Zap. nauchn. sem. POMI, 276, POMI, SPb., 2001, 83–111 (cited: 5) (cited: 3) ; V. N. Dubinin, E. V. Kostyuchenko, “Extremal problems in the function theory associated with the $n$-fold symmetry”, J. Math. Sci. (N. Y.), 118:1 (2003), 4778–4794
2000
68.
V. N. Dubinin, “Distortion theorems for polynomials on a circle”, Sb. Math., 191:12 (2000), 1797–1807 (cited: 4) (cited: 2)
69.
V. N. Dubinin, V. Yu. Kim, “Privedennye moduli i neravenstva dlya polinomov”, Analiticheskaya teoriya chisel i teoriya funktsii. 16, Zap. nauchn. sem. POMI, 263, POMI, SPb., 2000, 70–83 (cited: 6) (cited: 3) ; V. N. Dubinin, V. Yu. Kim, “Reduced moduli and inequalities for the polynomials”, J. Math. Sci. (New York), 110:6 (2002), 3070–3077
1999
70.
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
71.
V. N. Dubinin, “The majorization principle for $p$-valent functions”, Math. Notes, 65:4 (1999), 447–453 (cited: 3)
72.
V. N. Dubinin, E. V. Kostyuchenko, “The Teichm\ddot uller extremal problem and distortion theorems in the theory of univalent functions”, Siberian Math. J., 40:2 (1999), 258–261 (cited: 3)
1998
73.
V. N. Dubinin, E. G. Prilepkina, “Ob ekstremalnom razbienii prostranstvennykh oblastei”, Analiticheskaya teoriya chisel i teoriya funktsii. 15, Zap. nauchn. sem. POMI, 254, POMI, SPb., 1998, 95–107 (cited: 3) ; V. N. Dubinin, E. G. Prilepkina, “On extremal decomposition of $n$-space domains”, J. Math. Sci. (New York), 105:4 (2001), 2180–2189
74.
V. N. Dubinin, L. V. Kovalev, “Privedennyi modul kompleksnoi sfery”, Analiticheskaya teoriya chisel i teoriya funktsii. 15, Zap. nauchn. sem. POMI, 254, POMI, SPb., 1998, 76–94 (cited: 23) (cited: 11) ; V. N. Dubinin, L. V. Kovalev, “The reduced modulus of the complex sphere”, J. Math. Sci. (New York), 105:4 (2001), 2165–2179
1997
75.
V. N. Dubinin, “Asimptotika modulya vyrozhdayuschegosya kondensatora i nekotorye ee primeneniya”, Analiticheskaya teoriya chisel i teoriya funktsii. 14, Zap. nauchn. sem. POMI, 237, POMI, SPb., 1997, 56–73 (cited: 25) (cited: 19) ; V. N. Dubinin, “The asymptotics of module of a degenerating condenser and some of its applications”, J. Math. Sci. (New York), 95:3 (1999), 2209–2220
1996
76.
V. N. Dubinin, “Simmetrizatsiya, funktsiya Grina i konformnye otobrazheniya”, Analiticheskaya teoriya chisel i teoriya funktsii. 13, Zap. nauchn. sem. POMI, 226, POMI, SPb., 1996, 80–92 (cited: 5) (cited: 1) ; V. N. Dubinin, “Symmetrization, Green's function, and conformal mappings”, J. Math. Sci. (New York), 89:1 (1998), 967–975
77.
L. A. Aksent'ev, I. A. Aleksandrov, G. K. Antonyuk, V. A. Babeshko, V. Ya. Gutlyanskii, V. N. Dubinin, B. E. Levitsii, Yu. A. Mitropol'skii, Yu. G. Reshetnyak, Yu. E. Hohlov, “Igor Petrovich Mityuk (obituary)”, Russian Math. Surveys, 51:2 (1996), 315–316
1994
78.
V. N. Dubinin, “Symmetrization in the geometric theory of functions of a complex variable”, Russian Math. Surveys, 49:1 (1994), 1–79 (cited: 67)
79.
V. N. Dubinin, “Some properties of the reduced inner modulus”, Siberian Math. J., 35:4 (1994), 689–705 (cited: 6)
1991
80.
V. N. Dubinin, “Preobrazovaniya kondensatorov v $n$-mernom prostranstve”, Modulyarnye funktsii i kvadratichnye formy. 2, Zap. nauchn. sem. LOMI, 196, Nauka, SPb., 1991, 41–60 (cited: 2) (cited: 2) ; V. N. Dubinin, “Transformations of condensers in $n$-space”, J. Math. Sci., 70:6 (1994), 2085–2096
1988
81.
V. N. Dubinin, “Distortion theorem in the theory of conformal mappings”, Math. Notes, 44:3 (1988), 668–674 (cited: 1)
82.
V. N. Dubinin, “The separating transformation of domains and problems on the extremal partition”, Analytical theory of numbers and theory of functions. Part 9, Zap. Nauchn. Sem. LOMI, 168, “Nauka”, Leningrad. Otdel., Leningrad, 1988, 48–66
1987
83.
V. N. Dubinin, “Theorems on the covering of segments under a conformal mapping of an annulus”, Soviet Math. (Iz. VUZ), 31:9 (1987), 50–60
1986
84.
V. N. Dubinin, “An extremal problem for functions that are meromorphic in multiply connected domains”, Soviet Math. (Iz. VUZ), 30:10 (1986), 72–77
85.
V. N. Dubinin, “On covering theorems in the theory of analytic functions”, Analytical theory of numbers and theory of functions. Part 7, Zap. Nauchn. Sem. LOMI, 154, “Nauka”, Leningrad. Otdel., Leningrad, 1986, 67–75
1985
86.
V. N. Dubinin, “Transformation of functions and Dirichlet's principle”, Math. Notes, 38:1 (1985), 539–542 (cited: 5)
87.
V. N. Dubinin, “Metod simmetrizatsii v zadachakh o nenalegayuschikh oblastyakh”, Matem. sb., 128(170):1(9) (1985), 110–123 (cited: 6) (cited: 4) ; V. N. Dubinin, “The symmetrization method in problems on nonoverlapping domains”, Math. USSR-Sb., 56:1 (1987), 107–119
1984
88.
V. N. Dubinin, “Ob izmenenii garmonicheskoi mery pri simmetrizatsii”, Matem. sb., 124(166):2(6) (1984), 272–279 (cited: 12) (cited: 10) ; V. N. Dubinin, “On the change in harmonic measure under symmetrization”, Math. USSR-Sb., 52:1 (1985), 267–273
1980
89.
V. N. Dubinin, “Coverings of vertical segments under a conformal mapping”, Math. Notes, 28:1 (1980), 476–480 (cited: 2)
90.
V. N. Dubinin, “Geometric estimates of the Schwarzian derivative”, Uspekhi Mat. Nauk
91.
V. N. Dubinin, “Kraus inequality for multivalent functions”, Mat. Zametki (to appear)
2016
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