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, “Variational formulae for conformal capacity”, Sb. Math., 215:1 (2024), 90–100
2.
V. N. Dubinin, “Blaschke products and Smale's conjecture on complex polynomials”, Math. Notes, 116:2 (2024), 252–257
3.
V. N. Dubinin, “Teichmüller’s Modulsatz and the Variation of the Dirichlet Integral”, Siberian Mathematical Journal, 65:2 (2024), 289–294
4.
V. N. Dubinin, “Bounded holomorphic functions in a circular annulus”, Algebra i Analiz, 36:6 (2024), 30–46
5.
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
6.
V. N. Dubinin, “Green energy of discrete signed measure on concentric circles”, Izv. Math., 87:2 (2023), 265–283
7.
V. N. Dubinin, “Boundary Distortion and the Schwarzian Derivative of a Univalent Function in a Circular Annulus”, Math. Notes, 113:6 (2023), 776–783
8.
V. N. Dubinin, “On the dissymmetrization theorem”, Siberian Electronic Mathematical Reports, 20:1 (2023), 477–485
9.
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
10.
V. N. Dubinin, “An upper bound for the least critical values of finite Blaschke products”, Sb. Math., 213:6 (2022), 744–751
11.
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
12.
V. N. Dubinin, “On Holomorphic Coverings of Planar Domains”, Math. Notes, 112:5 (2022), 674–684
2021
13.
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
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
30.
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
31.
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
43.
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
44.
V. N. Dubinin, “Two-point boundary distortion estimate for Schwarzian derivative of holomorphic function”, FEMJ, 14:2 (2014), 191–199
45.
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
46.
V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892
47.
V. N. Dubinin, “On one extremal problem for complex polynomials with constraints on critical values”, Siberian Math. J., 55:1 (2014), 63–71
2015
48.
V. N. Dubinin, “Inequalities for moduli of the circumferentially mean $p$-valent functions”, J. Math. Sci. (N. Y.), 207:6 (2015), 832–838
49.
V. N. Dubinin, “Bounded holomorphic functions covering no concentric circles”, J. Math. Sci. (N. Y.), 207:6 (2015), 825–831
2014
50.
V. N. Dubinin, “Four-point distortion theorem for complex polynomials”, Complex Variables and Elliptic Equations, 59:1 (2014), 59–66
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, Condenser capacities and symmetrization in geometric function theory, Basel: Birkhauser / Springer, 2014 , xii+344 pp.
53.
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
54.
V. N. Dubinin, V. Yu. Kim, “Generalized condensers and boundary distortion theorems for conformal mappings”, FEMJ, 13:2 (2013), 196–208
55.
V. N. Dubinin, “Symmetrization of Condensers and Inequalities for Functions Multivalent in a Disk”, Math. Notes, 94:6 (2013), 876–884
2014
56.
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
57.
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
2012
58.
V. N. Dubinin, “On a Class of Univalent Functions”, FEMJ, 12:2 (2012), 184–194
2013
59.
V. N. Dubinin, “The Grötzsch and Teichmüller Extremal Problems on a Riemann Surface”, Math. Notes, 93:1 (2013), 50–57
2012
60.
V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684
61.
V. N. Dubinin, “A new version of circular symmetrization with applications to $p$-valent functions”, Sb. Math., 203:7 (2012), 996–1011
2013
62.
V. N. Dubinin, “Some inequalities for polynomials and rational functions associated with a lemniscate”, J. Math. Sci. (N. Y.), 193:1 (2013), 45–54
2012
63.
V. N. Dubinin, M. Vuorinen, “An extremal decomposition problem for harmonic measure”, Proceedings of the Amer.Math.Soc., 140:7 (2012), 2441–2446
V. N. Dubinin, D. A. Kirillova, “Some applications of extremal decompositions in the geometric function theory”, FEMJ, 10:2 (2010), 130–152
71.
V. N. Dubinin, “Steiner symmetrization and the initial coefficients of univalent functions”, Izv. Math., 74:4 (2010), 735–742
72.
V. N. Dubinin, “On the Finite-Increment Theorem for Complex Polynomials”, Math. Notes, 88:5 (2010), 647–654
73.
V. N. Dubinin, “Lower bounds for the half-plane capacity of compact sets and symmetrization”, Sb. Math., 201:11 (2010), 1635–1646
74.
V. N. Dubinin, E. G. Prilepkina, “Distortion theorems for univalent meromorphic functions on an annulus”, Siberian Math. J., 51:2 (2010), 229–243
2011
75.
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
76.
V. N. Dubinin, “Geometric versions of Schwarz lemma and symmetrization”, J. Math. Sci. (N. Y.), 178:2 (2011), 150–157
2010
77.
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
79.
V. N. Dubinin, “Quadratic forms involving Green's and Robin functions”, Sb. Math., 200:10 (2009), 1439–1452
2010
80.
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
81.
V. N. Dubinin, M. Vuorinen, “On conformal moduli of polygonal quadrilaters”, Israel J.Math., 171 (2009), 111 – 125
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
85.
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
86.
V. N. Dubinin, “Majorization Principles for Meromorphic Functions”, Math. Notes, 84:6 (2008), 751–755
87.
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
88.
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
89.
V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, J. Math. Sci. (N. Y.), 157:4 (2009), 573–583
2008
90.
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
92.
V. N. Dubinin, S. I. Kalmykov, “A majoration principle for meromorphic functions”, Sb. Math., 198:12 (2007), 1737–1745
2008
93.
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
94.
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
96.
V. N. Dubinin, “Lemniscates and Inequalities for the Logarithmic Capacities of Continua”, Math. Notes, 80:1 (2006), 31–35
97.
V. N. Dubinin, “Inequalities for critical values of polynomials”, Sb. Math., 197:8 (2006), 1167–1176
2007
98.
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
99.
V. N. Dubinin, “Capacities of condensers, generalizations of Grötzsch Lemmas, and symmetrization”, J. Math. Sci. (N. Y.), 143:3 (2007), 3053–3068
2005
100.
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
101.
V. N. Dubinin, “Polynomials with Critical Values on Intervals”, Math. Notes, 78:6 (2005), 768–772
102.
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
103.
V. N. Dubinin, S. I. Kalmykov, “Extremal properties of Chebyshev polynomials”, FEMJ, 5:2 (2004), 169–177
2006
104.
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
105.
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
106.
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
109.
V. N. Dubinin, N. V. Eyrikh, “The generalized reduced modulus”, FEMJ, 3:2 (2002), 150–164
110.
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
111.
V. N. Dubinin, “On an application of conformal maps to inequalities for rational functions”, Izv. Math., 66:2 (2002), 285–297
2004
112.
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
113.
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
114.
V. N. Dubinin, “Conformal mappings and inequalities for algebraic polynomials”, St. Petersburg Math. J., 13:5 (2002), 717–737
2001
115.
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
116.
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
117.
V. N. Dubinin, “Distortion theorems for polynomials on a circle”, Sb. Math., 191:12 (2000), 1797–1807
2002
118.
V. N. Dubinin, V. Yu. Kim, “Reduced moduli and inequalities for the polynomials”, J. Math. Sci. (New York), 110:6 (2002), 3070–3077
1999
119.
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
120.
V. N. Dubinin, “The majorization principle for $p$-valent functions”, Math. Notes, 65:4 (1999), 447–453
121.
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
122.
V. N. Dubinin, E. G. Prilepkina, “On extremal decomposition of $n$-space domains”, J. Math. Sci. (New York), 105:4 (2001), 2180–2189
123.
V. N. Dubinin, L. V. Kovalev, “The reduced modulus of the complex sphere”, J. Math. Sci. (New York), 105:4 (2001), 2165–2179
1998
124.
V. N. Dubinin, “Reduced moduli of open sets in the theory of analytic functions”, Dokl. Math., 58:3 (1998), 458-461
1999
125.
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
126.
V. N. Dubinin, “Symmetrization, Green's function, and conformal mappings”, J. Math. Sci. (New York), 89:1 (1998), 967–975
1996
127.
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
128.
V. N. Dubinin, “Symmetrization in the geometric theory of functions of a complex variable”, Russian Math. Surveys, 49:1 (1994), 1–79
129.
V. N. Dubinin, “Some properties of the reduced inner modulus”, Siberian Math. J., 35:4 (1994), 689–705
1993
130.
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
132.
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
133.
V. N. Dubinin, “On the covering of radial segments under conformal mapping of a disk”, Siberian Math. J., 31:2 (1990), 230–242
1988
134.
V. N. Dubinin, “Distortion theorem in the theory of conformal mappings”, Math. Notes, 44:3 (1988), 668–674
1991
135.
V. N. Dubinin, “A separating transformation of domains, and problems on extremal decomposition”, J. Soviet Math., 53:3 (1991), 252–263
1988
136.
V. N. Dubinin, The symmetrization method in geometric function theory, D. Sc. dissertation, Vladivostok, 1988
1987
137.
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
138.
V. N. Dubinin, “Transformation of condensers in space”, Soviet Math. Dokl., 36:2 (1988), 217-219
1986
139.
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
140.
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
143.
V. N. Dubinin, “The symmetrization method in problems on nonoverlapping domains”, Math. USSR-Sb., 56:1 (1987), 107–119
1985
144.
V. N. Dubinin, “On the change in harmonic measure under symmetrization”, Math. USSR-Sb., 52:1 (1985), 267–273
1980
145.
V. N. Dubinin, “Coverings of vertical segments under a conformal mapping”, Math. Notes, 28:1 (1980), 476–480
146.
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
147.
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
148.
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
149.
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
150.
V. N. Dubinin, “On Hayman’s conjecture”, Mathematical analysis, No. 3. Kuban Gos. Univ. Nauchn. Trudy, 217, 1976, 26-34
1974
151.
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
2024
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