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:
V. N. Dubinin, “On the change in harmonic measure under symmetrization”, Math. USSR-Sb., 52:1 (1985), 267–273
V. N. Dubinin, “Capacities and geometric transformations of subsets in n-space”, Geometric and Functional Analysis, 3:4 (1993), 342-369
V. N. Dubinin, “Symmetrization in the geometric theory of functions of a complex variable”, Russian Math. Surveys, 49:1 (1994), 1–79
V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials”, St. Petersburg Math. J., 13:5 (2002), 717–737
V. N. Dubinin, “Inequalities for critical values of polynomials”, Sb. Math., 197:8 (2006), 1167–1176
V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684
V. N. Dubinin, “On one extremal problem for complex polynomials with constraints on critical values”, Siberian Math. J., 55:1 (2014), 63–71
V. N. Dubinin, Condenser capacities and symmetrization in geometric function theory, Basel: Birkhauser / Springer, 2014 , xii+344 pp.
V. N. Dubinin, “Circular symmetrization of condensers on Riemann surfaces”, Sb. Math., 206:1 (2015), 61–86
V. N. Dubinin, “Geometric estimates for the Schwarzian derivative”, Russian Math. Surveys, 72:3 (2017), 479–511
V.N.Dubinin, E.G.Prilepkina, “Optimal Green energy points on the circles in d-space”, Journal of Mathematical Analysis and Applications, 499:2 (2021) (Article 125055)
2.
V.N.Dubinin, “Some remarks on rotation theorems for complex polynomials”, Siberian Electronic Mathematical Reports, 18:1 (2021), 369–376
3.
V. N. Dubinin, “Sharp Inequalities for Rational Functions on a Circle”, Math. Notes, 110:1 (2021), 41–47
2020
4.
V. N. Dubinin, “The Schwarzian Derivative of a
$p$-Valent Function”, Math. Notes, 107:6 (2020), 923–928
5.
V. N. Dubinin, Sibirsk. Mat. Zh., 61:4 (2020), 796–802
6.
V.N.Dubinin, “Pólya–Schur Inequality and the Green Energy of a Discrete Charge”, Doklady Mathematics, 101:3 (2020), 192–194
7.
V.N.Dubinin, “Distortion and Critical Values of the Finite Blaschke Product”, Constructive Approximation, 2020 (published online 18 September 2020)
2019
8.
V. N. Dubinin, “On the Dual Mean-Value Conjecture for Complex Polynomials”, Math. Notes, 106:1 (2019), 133–135
9.
V. N. Dubinin, “Circular symmetrization and Green function”, Dal'nevost. Mat. Zh., 19:1 (2019), 24–30
10.
V. N. Dubinin, “On holomorphic self-mappings of the unit disk”, Sib. elektron. matem. izv., 16 (2019), 1633–1639
11.
V. N. Dubinin, “Green energy and extremal decompositions”, Probl. anal. Issues Anal., 8(26):3 (2019), 38–44 (cited: 1);
2018
12.
V. N. Dubinin, “Some unsolved problems about condenser capacities on the plane”, Complex Analysis and Dynamical Systems, Ser.V: Trends in Mathematics. Editors: M.Agranovsky, A.Golberg,F.Jacobzon, D.Shoikhet, L.Zalcman, Birhauser, 2018, 81-92 (cited: 1) (cited: 2)
13.
V. N. Dubinin, “Two-point distortion theorems and the Schwarzian derivatives of meromorphic functions”, J. Math. Anal. Appl., 467:1 (2018), 371-378
14.
V. N. Dubinin, “Lemniscate Zone and Distortion Theorems for Multivalent Functions. II”, Math. Notes, 104:5 (2018), 683–688
15.
V. N. Dubinin, “Distortion theorem for complex polynomials”, Sib. elektron. matem. izv., 15 (2018), 1410–1415 (cited: 1) (cited: 1)
16.
L. A. Aksent'ev, A. I. Aptekarev, A. M. Bikchentaev, V. V. Goryainov, V. N. Dubinin, A. M. Elizarov, I. R. Kayumov, A. Laptev, S. R. Nasyrov, D. V. Prokhorov, A. G. Sergeev, V. D. Stepanov, “Farit Gabidinovich Avkhadiev (on his 70th birthday)”, Russian Math. Surveys, 73:1 (2018), 181–185
17.
A. I. Aptekarev, V. K. Beloshapka, V. I. Buslaev, V. V. Goryainov, V. N. Dubinin, V. A. Zorich, N. G. Kruzhilin, S. Yu. Nemirovski, S. Yu. Orevkov, P. V. Paramonov, S. I. Pinchuk, A. S. Sadullaev, A. G. Sergeev, S. P. Suetin, A. B. Sukhov, K. Yu. Fedorovskiy, A. K. Tsikh, “Evgenii Mikhailovich Chirka (on his 75th birthday)”, Russian Math. Surveys, 73:6 (2018), 1137–1144
2017
18.
V. N. Dubinin, “Geometric estimates for the Schwarzian derivative”, Russian Math. Surveys, 72:3 (2017), 479–511 (cited: 5) (cited: 3)
19.
V. N. Dubinin, “The Kraus Inequality for Multivalent Functions”, Math. Notes, 102:4 (2017), 516–520 (cited: 1) (cited: 1)
20.
V. N. Dubinin, A. S. Afanaseva-Grigoreva, “On the lemniscates of rational functions”, Dal'nevost. Mat. Zh., 17:2 (2017), 201–209
2018
21.
V. N. Dubinin, “Lemniscate Zone and Distortion Theorems for Multivalent Functions”, Journal of Mathematical Sciences (United States), 234:5 (2018), 598–607
2016
22.
V. N. Dubinin, “An Extremal Problem for the Derivative of a Rational Function”, Math. Notes, 100:5 (2016), 714–719 (cited: 4) (cited: 3)
2017
23.
V. N. Dubinin, “Critical values and moduli of derivative of a complex polynomial at its zeros”, J. Math. Sci. (N. Y.), 225:6 (2017), 877–882
2016
24.
V. N. Dubinin, “The logarithmic energy of zeros and poles of a rational function”, Siberian Math. J., 57:6 (2016), 981–986 (cited: 2) (cited: 4)
2015
25.
V. N. Dubinin, “Circular symmetrization of condensers on Riemann surfaces”, Sb. Math., 206:1 (2015), 61–86 (cited: 8) (cited: 4)
26.
V. N. Dubinin, “Schwarzian Derivative and Covering Arcs of a Pencil of Circles by Holomorphic Functions”, Math. Notes, 98:6 (2015), 920–925 (cited: 3) (cited: 3)
2016
27.
V. N. Dubinin, “Distortion theorems for circumferentially mean $p$-valent functions”, J. Math. Sci. (N. Y.), 217:1 (2016), 28–36
2015
28.
V. N. Dubinin, “Inequalities for harmonic measures with respect to non-overlapping domains”, Izv. Math., 79:5 (2015), 902–918 (cited: 3) (cited: 3)
29.
V. N. Dubinin, V. Y. Kim, “Covering theorem for p-valent functions with Montel's normalization”, Journal of Mathematical Analysis and Applications, 428:1 (2015), 502-507
30.
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
31.
V. N. Dubinin, “Two-point boundary distortion estimate for Schwarzian derivative of holomorphic function”, FEMJ, 14:2 (2014), 191–199
32.
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: 4) (cited: 1) (cited: 1) (cited: 4)
33.
V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892 (cited: 3) (cited: 1) (cited: 1) (cited: 3)
34.
V. N. Dubinin, “On one extremal problem for complex polynomials with constraints on critical values”, Siberian Math. J., 55:1 (2014), 63–71 (cited: 3) (cited: 5)
2015
35.
V. N. Dubinin, “Inequalities for moduli of the circumferentially mean $p$-valent functions”, J. Math. Sci. (N. Y.), 207:6 (2015), 832–838
36.
V. N. Dubinin, “Bounded holomorphic functions covering no concentric circles”, J. Math. Sci. (N. Y.), 207:6 (2015), 825–831 (cited: 19)
2014
37.
V. N. Dubinin, “Four-point distortion theorem for complex polynomials”, Complex Variables and Elliptic Equations, 59:1 (2014), 59–66 (cited: 3) (cited: 5)
38.
V. N. Dubinin, M. Vuorinen, “Ahlfors-Beurling conformal invariant and relative capacity of compact sets”, Proceedings of the Amer.Math.Soc., 142:11 (2014), 3865–3879 (cited: 4) (cited: 5)
39.
V. N. Dubinin, Condenser capacities and symmetrization in geometric function theory, Basel: Birkhauser / Springer, 2014 , xii+344 pp. (cited: 69)
40.
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
41.
V. N. Dubinin, V. Yu. Kim, “Generalized condensers and boundary distortion theorems for conformal mappings”, FEMJ, 13:2 (2013), 196–208
42.
V. N. Dubinin, “Symmetrization of Condensers and Inequalities for Functions Multivalent in a Disk”, Math. Notes, 94:6 (2013), 876–884 (cited: 2) (cited: 2) (cited: 2) (cited: 2)
2014
43.
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
2013
44.
V. N. Dubinin, “A Markov-type inequality and a lower bound for the moduli of critical values of polynomials”, Dokl. Math., 88:1 (2013), 449–450 (cited: 4) (cited: 4)
2012
45.
V. N. Dubinin, “On a Class of Univalent Functions”, FEMJ, 12:2 (2012), 184–194
2013
46.
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: 2) (cited: 1)
2012
47.
V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684 (cited: 14) (cited: 5) (cited: 5) (cited: 13)
48.
V. N. Dubinin, “A new version of circular symmetrization with applications to $p$-valent functions”, Sb. Math., 203:7 (2012), 996–1011 (cited: 7) (cited: 7) (cited: 7) (cited: 6)
2013
49.
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)
2012
50.
V. N. Dubinin, M. Vuorinen, “An extremal decomposition problem for harmonic measure”, Proceedings of the Amer.Math.Soc., 140:7 (2012), 2441–2446 (cited: 1) (cited: 1)
2011
51.
V. N. Dubinin, “On the distortion theorems for algebraic polynomials”, FEMJ, 11:1 (2011), 28–36
52.
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)
53.
V. N. Dubinin, “Boundary values of the Schwarzian derivative of a regular function”, Sb. Math., 202:5 (2011), 649–663 (cited: 5) (cited: 2) (cited: 2) (cited: 4)
2012
54.
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)
55.
V. N. Dubinin, “On the preservation of conformal capacity under meromorphic functions”, J. Math. Sci. (N. Y.), 184:6 (2012), 699–702 (cited: 2)
2011
56.
V. N. Dubinin, D. B. Karp, “Two-sided bounds for the logarithmic capacity of multiple intervals”, J. Anal. Math., 113 (2011), 227–239 (cited: 1) (cited: 2)
2010
57.
V. N. Dubinin, D. A. Kirillova, “Some applications of extremal decompositions in the geometric function theory”, FEMJ, 10:2 (2010), 130–152
58.
V. N. Dubinin, “Steiner symmetrization and the initial coefficients of univalent functions”, Izv. Math., 74:4 (2010), 735–742 (cited: 4) (cited: 1) (cited: 1) (cited: 2)
59.
V. N. Dubinin, “On the Finite-Increment Theorem for Complex Polynomials”, Math. Notes, 88:5 (2010), 647–654 (cited: 2) (cited: 2) (cited: 2) (cited: 3)
60.
V. N. Dubinin, “Lower bounds for the half-plane capacity of compact sets and symmetrization”, Sb. Math., 201:11 (2010), 1635–1646 (cited: 3) (cited: 1) (cited: 1) (cited: 2)
61.
V. N. Dubinin, E. G. Prilepkina, “Distortion theorems for univalent meromorphic functions on an annulus”, Siberian Math. J., 51:2 (2010), 229–243 (cited: 1) (cited: 1)
2011
62.
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)
63.
V. N. Dubinin, “Geometric versions of Schwarz lemma and symmetrization”, J. Math. Sci. (N. Y.), 178:2 (2011), 150–157 (cited: 5)
2010
64.
V. N. Dubinin, M. Vuorinen, “Robin functions and distortion theorems for regular mappings”, Math. Nachr., 283:11 (2010), 1589–1602 (cited: 7) (cited: 10)
2009
65.
V. N. Dubinin, “Condenser capacity and symmetrization in the extremal decomposition problems”, FEMJ, 9:1-2 (2009), 84–93
66.
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)
2010
67.
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
2009
68.
V. N. Dubinin, M. Vuorinen, “On conformal moduli of polygonal quadrilaters”, Israel J.Math., 171 (2009), 111 – 125 (cited: 7) (cited: 8)
69.
V. N. Dubinin, T. Sugawa, “Dual mean value problem for complex polynomials”, Proc. Japan. Acad. Ser.A, Math.Sci., 85:9 (2009), 135 – 137 (cited: 4) (cited: 5)
70.
V. N. Dubinin, Condenser capacity and symmetrization in the geometric function theory of a complex variable, Dalnauka, Vladivostok, 2009 , 401 pp. https://scholar.google.ru/scholar?hl=ru&as_sdt=0,5&cluster=18224154641338161455
71.
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
72.
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
73.
V. N. Dubinin, “Majorization Principles for Meromorphic Functions”, Math. Notes, 84:6 (2008), 751–755 (cited: 4) (cited: 3) (cited: 3) (cited: 3)
74.
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
75.
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
2009
76.
V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, J. Math. Sci. (N. Y.), 157:4 (2009), 573–583
2008
77.
V. N. Dubinin, D. B. Karp, “Capacities of certain plane condensers and sets under simple geometric transformations”, Complex Variables and Elliptic Equations, 53:6 (2008), 607 – 622 (cited: 6)
2007
78.
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
79.
V. N. Dubinin, S. I. Kalmykov, “A majoration principle for meromorphic functions”, Sb. Math., 198:12 (2007), 1737–1745 (cited: 4) (cited: 6) (cited: 6) (cited: 2)
2008
80.
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: 1) (cited: 3)
2007
81.
V. N. Dubinin, D. B. Karp, “Generalized condensers and distortion theorems for conformal mappings of planar domains”, In: The Interaction of Analysis and Geometry, Edited by: V.I.Burenkov, T.Iwaniec, and S.K.Vodopyanov, AMS Contemporary Mathematics, 424, AMER MATHEMATICAL SOC, P.O. BOX 6248, PROVIDENCE, RI 02940 USA, 2007, 33-51 (cited: 6)
82.
V. N. Dubinin, E. G. Prilepkina, “On variational principles of conformal mappings”, St. Petersburg Math. J., 18:3 (2007), 373–389 (cited: 1)
2006
83.
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)
84.
V. N. Dubinin, “Inequalities for critical values of polynomials”, Sb. Math., 197:8 (2006), 1167–1176 (cited: 5) (cited: 8) (cited: 8) (cited: 6)
2007
85.
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) (cited: 19)
86.
V. N. Dubinin, “Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization”, J. Math. Sci. (N. Y.), 143:3 (2007), 3053–3068 (cited: 1)
2005
87.
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
88.
V. N. Dubinin, “Polynomials with Critical Values on Intervals”, Math. Notes, 78:6 (2005), 768–772 (cited: 1) (cited: 1) (cited: 1) (cited: 1)
89.
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: 6) (cited: 2) (cited: 2) (cited: 5)
2004
90.
V. N. Dubinin, S. I. Kalmykov, “Extremal properties of Chebyshev polynomials”, FEMJ, 5:2 (2004), 169–177
2006
91.
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) (cited: 5) (cited: 8)
2005
92.
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 (cited: 4)
93.
V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials. II”, J. Math. Sci. (N. Y.), 129:3 (2005), 3823–3834 (cited: 2)
2003
94.
V. N. Dubinin, Capacities of condensers in the geometric function theory, Far Eastern State University, Vladivostok, 2003 , 116 pp. https://scholar.google.com/scholar?cluster=12018319739435650108&hl=en&oi=scholarr
95.
V. N. Dubinin, “Symmetrization methods in the geometric function theory”, Trudy po geometrii i analizu, Iz-vo Mat. Inst., Novosibirsk, 2003, 126–150
2002
96.
V. N. Dubinin, N. V. Eyrikh, “The generalized reduced modulus”, FEMJ, 3:2 (2002), 150–164
97.
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
98.
V. N. Dubinin, “On an application of conformal maps to inequalities for rational functions”, Izv. Math., 66:2 (2002), 285–297 (cited: 5)
2004
99.
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
100.
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
2002
101.
V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials”, St. Petersburg Math. J., 13:5 (2002), 717–737
2001
102.
V. N. Dubinin, V. Yu. Kim, “Averaging transformation of sets and functions on Riemann surfaces”, Russian Math. (Iz. VUZ), 45:5 (2001), 19–27
2003
103.
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
104.
V. N. Dubinin, “Distortion theorems for polynomials on a circle”, Sb. Math., 191:12 (2000), 1797–1807 (cited: 6) (cited: 6)
2002
105.
V. N. Dubinin, V. Yu. Kim, “Reduced moduli and inequalities for the polynomials”, J. Math. Sci. (New York), 110:6 (2002), 3070–3077 (cited: 3)
1999
106.
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
107.
V. N. Dubinin, “The majorization principle for $p$-valent functions”, Math. Notes, 65:4 (1999), 447–453 (cited: 3) (cited: 1)
108.
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) (cited: 3)
2001
109.
V. N. Dubinin, E. G. Prilepkina, “On extremal decomposition of $n$-space domains”, J. Math. Sci. (New York), 105:4 (2001), 2180–2189 (cited: 4)
110.
V. N. Dubinin, L. V. Kovalev, “The reduced modulus of the complex sphere”, J. Math. Sci. (New York), 105:4 (2001), 2165–2179 (cited: 9)
1998
111.
V. N. Dubinin, “Reduced moduli of open sets in the theory of analytic functions”, Dokl. Math., 58:3 (1998), 458-461 (cited: 2) (cited: 2)
1999
112.
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 (cited: 8)
1998
113.
V. N. Dubinin, “Symmetrization, Green's function, and conformal mappings”, J. Math. Sci. (New York), 89:1 (1998), 967–975 (cited: 6)
1996
114.
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
115.
V. N. Dubinin, “Symmetrization in the geometric theory of functions of a complex variable”, Russian Math. Surveys, 49:1 (1994), 1–79 (cited: 85) (cited: 49)
116.
V. N. Dubinin, “Some properties of the reduced inner modulus”, Siberian Math. J., 35:4 (1994), 689–705 (cited: 7) (cited: 6)
1993
117.
V. N. Dubinin, “Capacities and geometric transformations of subsets in n-space”, Geometric and Functional Analysis, 3:4 (1993), 342-369 (cited: 25)
1994
118.
V. N. Dubinin, “Transformations of condensers in $n$-space”, J. Math. Sci., 70:6 (1994), 2085–2096 (cited: 1)
1990
119.
V. N. Dubinin, “On the question of construction of symmetrization transformations”, Mathematical physics and mathematical simulation in ecology, 1, Far-Eastern Branch of the USSR Acad. Sci., Vladivostok, 1990, 55-69
120.
V. N. Dubinin, “On the covering of radial segments under conformal mapping of a disk”, Siberian Math. J., 31:2 (1990), 230–242 (cited: 1) (cited: 1) (cited: 1)
1988
121.
V. N. Dubinin, “Distortion theorem in the theory of conformal mappings”, Math. Notes, 44:3 (1988), 668–674 (cited: 1) (cited: 1)
1991
122.
V. N. Dubinin, “A separating transformation of domains, and problems on extremal decomposition”, J. Soviet Math., 53:3 (1991), 252–263 (cited: 7)
1988
123.
V. N. Dubinin, The symmetrization method in geometric function theory, D. Sc. dissertation, Vladivostok, 1988
1987
124.
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
1988
125.
V. N. Dubinin, “Transformation of condensers in space”, Soviet Math. Dokl., 36:2 (1988), 217-219 (cited: 8)
1986
126.
V. N. Dubinin, “An extremal problem for functions that are meromorphic in multiply connected domains”, Soviet Math. (Iz. VUZ), 30:10 (1986), 72–77
1988
127.
V. N. Dubinin, “On covering theorems in the theory of analytic functions”, J. Soviet Math., 43:4 (1988), 2553–2558
1986
128.
V. N. Dubinin, “A symmetrization method and transfinite diameter”, Siberian Mathematical Journal, 27:2 (1986), 174-180 https://link.springer.com/content/pdf/10.1007/BF00969383.pdf (cited: 3) (cited: 3) (cited: 3)
1985
129.
V. N. Dubinin, “Transformation of functions and Dirichlet's principle”, Math. Notes, 38:1 (1985), 539–542 (cited: 5) (cited: 4)
1987
130.
V. N. Dubinin, “The symmetrization method in problems on nonoverlapping domains”, Math. USSR-Sb., 56:1 (1987), 107–119 (cited: 2)
1985
131.
V. N. Dubinin, “On the change in harmonic measure under symmetrization”, Math. USSR-Sb., 52:1 (1985), 267–273
1980
132.
V. N. Dubinin, “Coverings of vertical segments under a conformal mapping”, Math. Notes, 28:1 (1980), 476–480 (cited: 2) (cited: 2)
133.
V. N. Dubinin, “Some covering theorems in the theory of analytic functions”, Differential equations and functional analysis, Far-Eastern Science Centre, Acad. Sci. USSR, Vladivostok, 1980, 98-109
1978
134.
V. N. Dubinin, “The product of internal radii of “partially nonoverlapping” domains”, Questions in the metric theory of mappings and its application (Proc. Fifth Colloq. Quasiconformal Mappings, Generalizations Appl., Donetsk, 1976), Naukova Dumka, Kiev, 1978, 24-31
1977
135.
V. N. Dubinin, Some symmetrization transformations and covering theorems in the geometric theory of functions of a complex variable, Candidate’s dissertation, Krasnodar, 1977
1976
136.
V. N. Dubinin, “Some symmetrization transformations and their applications to covering theorems”, Mathematical analysis, No. 3. Kuban. Gos. Univ. Nauchn. Trudy, 217, 1976, 17-25
137.
V. N. Dubinin, “On Hayman’s conjecture”, Mathematical analysis, No. 3. Kuban Gos. Univ. Nauchn. Trudy, 217, 1976, 26-34
1974
138.
V. N. Dubinin, “A certain symmetrization method”, Mathematical analysis, No. 2. Kuban. Gos. Univ. Naučn. Trudy, 180, Kuban. Gos. Univ., 1974, 50-64
A capacity look at the Schwarzian derivative V. N. Dubinin The 27th International Conference on Finite and Infinite Dimensional Complex Analysis and Applications August 14, 2019 10:30
2021
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