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, “Inequalities for polynomials with real critical values”, Izv. RAN. Ser. Mat. (to appear)
2025
2.
V. N. Dubinin, “On lemniscates and critical points of finite Blaschke products”, Math. Notes, 118:3 (2025), 550–555
2024
3.
V. N. Dubinin, “Variational formulae for conformal capacity”, Sb. Math., 215:1 (2024), 90–100
4.
V. N. Dubinin, “Blaschke products and Smale's conjecture on complex polynomials”, Math. Notes, 116:2 (2024), 252–257
5.
V. N. Dubinin, “Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral”, Siberian Mathematical Journal, 65:2 (2024), 289–294
6.
V. N. Dubinin, “Bounded holomorphic functions in a circular annulus”, Algebra i Analiz, 36:6 (2024), 30–46
7.
V. N. Dubinin, “Inequalities for derivatives of rational functions with critical values on an interval”, Dal'nevost. Mat. Zh., 24:2 (2024), 187–192
2023
8.
V. N. Dubinin, “Green energy of discrete signed measure on concentric circles”, Izv. Math., 87:2 (2023), 265–283
9.
V. N. Dubinin, “Boundary Distortion and the Schwarzian Derivative of a Univalent Function in a Circular Annulus”, Math. Notes, 113:6 (2023), 776–783
10.
V. N. Dubinin, “On the dissymmetrization theorem”, Siberian Electronic Mathematical Reports, 20:1 (2023), 477–485
11.
V. N. Dubinin, “An asymptotic formula for the capacity of a condenser when all its plates are degenerate”, Dal'nevost. Mat. Zh., 23:2 (2023), 184–189
2022
12.
V. N. Dubinin, “An upper bound for the least critical values of finite Blaschke products”, Sb. Math., 213:6 (2022), 744–751
13.
V. N. Dubinin, V. Yu. Kim, “On the condensers with variable plates, potential levels and domain of definition”, Dal'nevost. Mat. Zh., 22:1 (2022), 55–60
14.
V. N. Dubinin, “On Holomorphic Coverings of Planar Domains”, Math. Notes, 112:5 (2022), 674–684
2021
15.
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)
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
V. N. Dubinin, “Geometric estimates for the Schwarzian derivative”, Russian Math. Surveys, 72:3 (2017), 479–511
32.
V. N. Dubinin, “The Kraus Inequality for Multivalent Functions”, Math. Notes, 102:4 (2017), 516–520
33.
V. N. Dubinin, A. S. Afanaseva-Grigoreva, “On the lemniscates of rational functions”, Dal'nevost. Mat. Zh., 17:2 (2017), 201–209
2018
34.
V. N. Dubinin, “Lemniscate Zone and Distortion Theorems for Multivalent Functions”, Journal of Mathematical Sciences (United States), 234:5 (2018), 598–607
2016
35.
V. N. Dubinin, “An Extremal Problem for the Derivative of a Rational Function”, Math. Notes, 100:5 (2016), 714–719
2017
36.
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
37.
V. N. Dubinin, “The logarithmic energy of zeros and poles of a rational function”, Siberian Math. J., 57:6 (2016), 981–986
2015
38.
V. N. Dubinin, “Circular symmetrization of condensers on Riemann surfaces”, Sb. Math., 206:1 (2015), 61–86
39.
V. N. Dubinin, “Schwarzian Derivative and Covering Arcs of a Pencil of Circles by Holomorphic Functions”, Math. Notes, 98:6 (2015), 920–925
2016
40.
V. N. Dubinin, “Distortion theorems for circumferentially mean $p$-valent functions”, J. Math. Sci. (N. Y.), 217:1 (2016), 28–36
2015
41.
V. N. Dubinin, “Inequalities for harmonic measures with respect to non-overlapping domains”, Izv. Math., 79:5 (2015), 902–918
42.
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
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
V. N. Dubinin, D. A. Kirillova, “Some applications of extremal decompositions in the geometric function theory”, FEMJ, 10:2 (2010), 130–152
69.
V. N. Dubinin, “Steiner symmetrization and the initial coefficients of univalent functions”, Izv. Math., 74:4 (2010), 735–742
70.
V. N. Dubinin, “On the Finite-Increment Theorem for Complex Polynomials”, Math. Notes, 88:5 (2010), 647–654
71.
V. N. Dubinin, “Lower bounds for the half-plane capacity of compact sets and symmetrization”, Sb. Math., 201:11 (2010), 1635–1646
72.
V. N. Dubinin, E. G. Prilepkina, “Distortion theorems for univalent meromorphic functions on an annulus”, Siberian Math. J., 51:2 (2010), 229–243
2011
73.
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
74.
V. N. Dubinin, “Geometric versions of Schwarz lemma and symmetrization”, J. Math. Sci. (N. Y.), 178:2 (2011), 150–157
2010
75.
V. N. Dubinin, M. Vuorinen, “Robin functions and distortion theorems for regular mappings”, Math. Nachr., 283:11 (2010), 1589–1602
V. N. Dubinin, “Condenser capacity and symmetrization in the extremal decomposition problems”, FEMJ, 9:1-2 (2009), 84–93
77.
V. N. Dubinin, “Quadratic forms involving Green's and Robin functions”, Sb. Math., 200:10 (2009), 1439–1452
2010
78.
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
79.
V. N. Dubinin, M. Vuorinen, “On conformal moduli of polygonal quadrilaters”, Israel J.Math., 171 (2009), 111 – 125
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
83.
V. N. Dubinin, “Majorization Principles for Meromorphic Functions”, Math. Notes, 84:6 (2008), 751–755
84.
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
85.
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
86.
V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, J. Math. Sci. (N. Y.), 157:4 (2009), 573–583
2008
87.
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
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
89.
V. N. Dubinin, S. I. Kalmykov, “A majoration principle for meromorphic functions”, Sb. Math., 198:12 (2007), 1737–1745
2008
90.
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
2007
91.
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
V. N. Dubinin, E. G. Prilepkina, “On variational principles of conformal mappings”, St. Petersburg Math. J., 18:3 (2007), 373–389
2006
93.
V. N. Dubinin, “Lemniscates and Inequalities for the Logarithmic Capacities of Continua”, Math. Notes, 80:1 (2006), 31–35
94.
V. N. Dubinin, “Inequalities for critical values of polynomials”, Sb. Math., 197:8 (2006), 1167–1176
2007
95.
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
96.
V. N. Dubinin, “Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization”, J. Math. Sci. (N. Y.), 143:3 (2007), 3053–3068
2005
97.
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
98.
V. N. Dubinin, “Polynomials with Critical Values on Intervals”, Math. Notes, 78:6 (2005), 768–772
99.
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
2004
100.
V. N. Dubinin, S. I. Kalmykov, “Extremal properties of Chebyshev polynomials”, FEMJ, 5:2 (2004), 169–177
2006
101.
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
2005
102.
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
103.
V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials. II”, J. Math. Sci. (N. Y.), 129:3 (2005), 3823–3834
V. N. Dubinin, “Symmetrization methods in the geometric function theory”, Trudy po geometrii i analizu, Iz-vo Mat. Inst., Novosibirsk, 2003, 126–150
2002
106.
V. N. Dubinin, N. V. Eyrikh, “The generalized reduced modulus”, FEMJ, 3:2 (2002), 150–164
107.
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
108.
V. N. Dubinin, “On an application of conformal maps to inequalities for rational functions”, Izv. Math., 66:2 (2002), 285–297
2004
109.
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
110.
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
111.
V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials”, St. Petersburg Math. J., 13:5 (2002), 717–737
2001
112.
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
113.
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
114.
V. N. Dubinin, “Distortion theorems for polynomials on a circle”, Sb. Math., 191:12 (2000), 1797–1807
2002
115.
V. N. Dubinin, V. Yu. Kim, “Reduced moduli and inequalities for the polynomials”, J. Math. Sci. (New York), 110:6 (2002), 3070–3077
1999
116.
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
117.
V. N. Dubinin, “The majorization principle for $p$-valent functions”, Math. Notes, 65:4 (1999), 447–453
118.
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
2001
119.
V. N. Dubinin, E. G. Prilepkina, “On extremal decomposition of $n$-space domains”, J. Math. Sci. (New York), 105:4 (2001), 2180–2189
120.
V. N. Dubinin, L. V. Kovalev, “The reduced modulus of the complex sphere”, J. Math. Sci. (New York), 105:4 (2001), 2165–2179
1998
121.
V. N. Dubinin, “Reduced moduli of open sets in the theory of analytic functions”, Dokl. Math., 58:3 (1998), 458-461
1999
122.
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
1998
123.
V. N. Dubinin, “Symmetrization, Green's function, and conformal mappings”, J. Math. Sci. (New York), 89:1 (1998), 967–975
1994
124.
V. N. Dubinin, “Symmetrization in the geometric theory of functions of a complex variable”, Russian Math. Surveys, 49:1 (1994), 1–79
125.
V. N. Dubinin, “Some properties of the reduced inner modulus”, Siberian Math. J., 35:4 (1994), 689–705
1993
126.
V. N. Dubinin, “Capacities and geometric transformations of subsets in n-space”, Geometric and Functional Analysis, 3:4 (1993), 342-369
V. N. Dubinin, “Transformations of condensers in $n$-space”, J. Math. Sci., 70:6 (1994), 2085–2096
1990
128.
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
129.
V. N. Dubinin, “On the covering of radial segments under conformal mapping of a disk”, Siberian Math. J., 31:2 (1990), 230–242
1988
130.
V. N. Dubinin, “Distortion theorem in the theory of conformal mappings”, Math. Notes, 44:3 (1988), 668–674
1991
131.
V. N. Dubinin, “A separating transformation of domains, and problems on extremal decomposition”, J. Soviet Math., 53:3 (1991), 252–263
1988
132.
V. N. Dubinin, The symmetrization method in geometric function theory, D. Sc. dissertation, Vladivostok, 1988
1987
133.
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
134.
V. N. Dubinin, “Transformation of condensers in space”, Soviet Math. Dokl., 36:2 (1988), 217-219
1986
135.
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
136.
V. N. Dubinin, “On covering theorems in the theory of analytic functions”, J. Soviet Math., 43:4 (1988), 2553–2558
V. N. Dubinin, “Transformation of functions and Dirichlet's principle”, Math. Notes, 38:1 (1985), 539–542
1987
139.
V. N. Dubinin, “The symmetrization method in problems on nonoverlapping domains”, Math. USSR-Sb., 56:1 (1987), 107–119
1985
140.
V. N. Dubinin, “On the change in harmonic measure under symmetrization”, Math. USSR-Sb., 52:1 (1985), 267–273
1980
141.
V. N. Dubinin, “Coverings of vertical segments under a conformal mapping”, Math. Notes, 28:1 (1980), 476–480
142.
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
143.
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
144.
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
145.
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
146.
V. N. Dubinin, “On Hayman’s conjecture”, Mathematical analysis, No. 3. Kuban Gos. Univ. Nauchn. Trudy, 217, 1976, 26-34
1974
147.
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
2025