Selected papers, listed by topics

See also: chronological listing of all papers.

Analytic theory of differential equations

  1. pdf Meromorphic solutions of algebraic differential equations. English translation: Russian Math. Surveys, 37, 4 (1982), 61-95. Correction: 38, 6 (1983).
  2. pdf An elementary remark on the set of entire solutions of a system of ordinary differential equations, ``Functional Analysis and Applied Mathematics'', Kiev, Naukova Dumka, 1982, 31-32 (Russian).
  3. pdf On meromorphic solutions of algebraic differential equations of 1-st order. English translation: Functional Analysis and its Applications, 18, 3 (1984), 246-248.
  4. pdf (Russian) Meromorphic solutions of equations of Briot-Bouquet type. English translation: Amer. Math. Soc. Transl. (2) Vol. 133 (1986), 15-23.
  5. pdf Rational solutions of first-order differential equations, Ann. Acad. Sci. Fenn., Math., v. 23, 1998, 181-190. Corrected version.
  6. pdf Meromorphic traveling wave solutions of the Kuramoto-Sivashinsky equation, J. Math. Phys., Anal. Geom. (Kharkov), 2 (2006) N 3 278-286.
  7. pdf (with A. Gabrielov and B. Shapiro) High energy eigenfunctions of one-dimensional Schrödinger operators with polynomial coefficients, Computational Methods and Function Theory, 8 (2008). No. 2, 513--529.
  8. pdf (with A. Gabrielov and B. Shapiro) Zeros of eigenfunctions of some anharmonic oscillators, Ann. Inst. Fourier, Grenoble, 58, 2 (2008) 603-624.
  9. pdf (with L. W. Liao and T. W. Ng) Meromorphic solutions of higher order Briot-Bouquet differential equations, Math. Proc. Cambridge Philos. Soc., v. 146, no. 1 (2009) 197-206.
  10. pdf (with A. Gabrielov) Analytic continuation of eigenvalues of a quartic oscillator, Comm. Math. Phys., v. 287, No. 2 (2009) 431-457.
  11. pdf (with A. Gabrielov) Singluar perturbation of polynomial potentials in the complex domain with applications to spectral loci of PT-symmetric families, Moscow Math. J., 11, 3, (2011) 473-503.
  12. pdf (with A. Gabrielov) Quasi-exactly solvable quartic: elementary integrals and asymptotics, J. Phys. A: Math. Theor. 44 (2011) 312001.
  13. pdf (with A. Gabrielov and A. Hinkkanen) Exceptional solutions of the Painleve VI equation, J. Math. Phys., 58, 1 (2017).
  14. pdf (with A. Gabrielov) Circular pentagons and real solutions of Painleve VI equations, Comm. Math. Phys., 355, 1 (2017) 51-95.
  15. pdf (with W. Bergweiler) On the Bank-Laine conjecture, J.European Math. Soc., 19 (2017) 6, 1899-1909.
  16. pdf (with V. Tarasov) Fuchsian equations with three non-apparent singularities, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 14 (2018), 058, 12p.
  17. pdf (with A. Gabrielov) PT-symmetric eigenvalues for homogeneous potentials, J. Math. Phys., 59 (2018) 053503.
  18. pdf (with W. Bergweiler) Quasiconformal surgery and linear differential equations, J. d'Analyse, 137 (2019) 2, 751-812
  19. pdf (with A. Gabrielov, G. Mondello and D. Panov) Moduli spaces for Lame functions and Abelian integrals of the second kind, Comm. Contemp. Math., 24, (2022) N2, 2150028, 1-68.

Exact inequalities: extremal problems for polynomials, entire and meromorphic functions

  1. pdf On entire functions bounded on the real axis, Dokl. AN SSSR, 37 (1988), 692-695.
  2. pdf (with L. Lempert) An extremal problem for polynomials, Proc. AMS, 122, 1 (1994) 191-193.
  3. pdf (with W. Hayman) On the length of lemniscates, Michigan Math. J., 46 (1999) 409--415.
  4. pdf (with M. Bonk) Covering properties of meromorphic functions, negative curvature and spherical geometry, Ann of Math. 152 (2000), 551-592.
  5. pdf Transcendental meromorphic functions with three singular values, Illinois J. Math., 48 (2004), 701-709.
  6. pdf (with A. Baernstein II, A. Fryntov and A. Solynin) Sharp estimates for hyperbolic metrics and covering theorems of Landau type, Ann. ASF 30 (2005) 113-133.
  7. pdf A Markov-type inequality for arbitrary plane continua, Proc AMS, 2006.
  8. pdf (with P. Yuditskii) Uniform approximation of sgn(x) by polynomials and entire functions, J. d'Analyse, 101 (2007) 313-324.
  9. pdf (with P. Yuditskii) Extremal problem for a class of entire functions, CRAS. Ser. I, 346 (2008) 825-828.
  10. pdf (with P. Yuditskii) Polynomials of the best uniform approximation to sgn(x) on two intervals, J. d'Analyse math., 114 (2011) 285-315.
  11. pdf (with W. Bergweiler) Goldberg's constants, J. d'Analyse Math. 119, 1, (2013) 365-402. Maple script related to this paper
  12. pdf (with A. Fryntov) Remarks on Obrechkoff's inequality, Proc. AMS 144 (2016) 703-707.

Real rational functions, Real algebraic geometry, Control theory.

  1. pdf (with A. Gabrielov) Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry, Ann of Math., 155 (2002), 105-129.
  2. pdf (with A. Gabrielov) Degrees of real Wronski maps, Discrete and computational geometry, 28 (2002) 331-347.
  3. pdf (with A. Gabrielov) Pole placement by static output feedback for generic linear systems, SIAM J. on Control and Opt., 41, 1 (2002) 303--312.
  4. pdf (with A. Gabrielov) Elementary proof of the B. and M. Shapiro conjecture for rational functions.
  5. pdf (with A. Gabrielov, M. Shapiro and A. Vainshtein) Rational functions and real Schubert calculus, Proc. AMS, 134 (2006), no. 4, 949--957.

Value distribution of meromorphic functions

  1. pdf (with M. Sodin) A hypothesis of Littlewood and the distribution of values of entire functions. English translation: Functional Analysis and Appl., 20, N 1 (1986), 60-62.
  2. pdf Inverse problem of value distribution theory for meromorphic functions of finite order. English translation: Siberian Math. J., 27, 3 (1987), 377-390.
  3. pdf Lower estimates in Littlewood's conjecture on mean spherical derivative of a polynomial. Proc. Amer. Math. Soc., 112, N 3 (1991), 713-715.
  4. pdf A counterexample to the Arakelyan Conjecture. Bull. Amer. Math. Soc. 1992, vol. 27, N 1, p. 159-164.
  5. pdf and djvu Meromorphic functions with small ramification, Indiana University Math. Journal, 42, 4 (1993), 1193-1218.
  6. pdf (with W. Bergweiler) On the singularities of the inverse to a meromorphic function of finite order, Revista math. iberoamericana, 11 (1995), 355-373.

Geometric theory of meromorphic functions.

  1. pdf (with W. Bergweiler) On the singularities of the inverse to a meromorphic function of finite order, Revista math. iberoamericana, 11 (1995), 355-373.
  2. pdf (with M. Bonk) Covering properties of meromorphic functions, negative curvature and spherical geometry, Ann of Math. 152 (2000), 551-592.
  3. pdf Transcendental meromorphic functions with three singular values, Illinois J. Math., 48 (2004), 701-709.

Asymptotic values and asymptotic curves

  1. pdf The set of asymptotic values of a meromorphic function of finite order. English translation: Math. Notes, 24, 5-6 (1979), 914-916.
  2. pdf Growth of subharmonic functions on asymptotic curves. English translation: Soviet Math. Dokl., 20, 5 (1979), 943-945.
  3. pdf (with A. Goldberg) Asymptotic curves of entire functions of finite order. English translation: Math. Sbornik, 37, 4 (1980), 509-533.

Real entire functions

  1. pdf (with W. Bergweiler and J. Langley) Real entire functions of infinite order and a conjecture of Wiman, GAFA, 13 (2003), 975-991.
  2. pdf (with W. Bergweiler) Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions, 2005 Acta math., 197, 2 (2006), 125-146.

Meromorphic functons with a-points on rays

  1. pdf (with W. Bergweiler) Meromorphic functions with linearly distributed values and Julia sets of rational functions, Proc. AMS. 137 (2009), 2329-2333.
  2. pdf (with W. Bergweiler and A. Hinkkanen) Entire functions with two radially distributed values, Math. Proc. Cambridge Phil. Soc., 165 (2018), 93-108.
  3. pdf (with W. Bergweiler) Radially distributed values and normal families, IMRN, vol. 2019, (2019) 23, 7356–7378.
  4. pdf (with W. Bergweiler) Radially distributed values and normal families, II, J. d'Analyse, 141 (2020) 99-111.
  5. pdf (with W. Bergweiler) Entire functions with separated zeros and 1-points, Comp. Methods and Function Theory, 20 (3) (2020) 729-746.
  6. pdf (with W. Bergweiler) Meromorphic functions with radially distributed values, CMFT.

Holomorphic curves in projective space.

  1. pdf (with M. Sodin) Value distribution of meromorphic functions and meromorphic curves from the point of view of potential theory. Algebra & Analysis, 3, N 1 (1991), 131-164. (Russian). (English translation: St. Petersburg Math. J., 3 (1992), 109-136.)
  2. pdf Holomorphic curves omitting five planes in projective space, American J. Math., 118, 6 (1996), 1141-1151.
  3. pdf Value distribution and potential theory, Proceedings of the International Congress of Mathematicians, vol. 2, p. 681-690, Higher Education Press, Beijing, 2002.
  4. pdf (with M. Barrett) A generalization of a theorem of Clunie and Hayman, Proc. Amer. Math. Soc., 140, (2012) 1397-1402.

Iteration of analytic functions and functional equations

  1. pdf (with M. Lyubich) Examples of entire functions with pathological dynamics. J. London Math. Soc., (2) 36 (1987), 458-468.
  2. pdf On the iteration of entire functions, in: Dynamical Systems and Ergodic Theory. Banach Center Publications, 23, Warszawa, PWN, 1989, 339-345.
  3. pdf Some functional equations related to iteration of rational functions. Algebra and Analysis, 1, 4 (1989), 102-116 (Russian). Leningrad Math. J., 1, 4 (1990), 905-919 (English).
  4. pdf (with M. Lyubich) Dynamical properties of some classes of entire functions. Ann. Inst. Fourier, 42, 4 (1992), p. 1-32.
  5. pdf (with W. Bergweiler) Meromorphic functions with linearly distributed values and Julia sets of rational functions, Proc. AMS. 137 (2009), 2329-2333.
  6. pdf Invariant curves and semiconjugacies of rational functions, Fundamenta Math., 219, 3 (2012) 263-270.

Quasiconformal and quasiregular mappings

  1. pdf (with J. Lewis) Uniform limits of certain A-harmonic functions with applications to quasiregular mappings. Ann. Acad. Sci. Fenn., Ser. A. I., 1991, vol. 16, fasc. 2, 361-375.
  2. pdf (with D. Hamilton) On the area distortion by quasiconformal mappings, Proc. AMS, 123, 9 (1995), 2793-2797.

Metrics of constant positive curvature with conic singularities

  1. pdf Metrics of positive curvature with conic singularities on the sphere, Proc. AMS, 132 (2004), 11, 3349--3355.
  2. pdf (with W. Bergweiler) Green functions and antiholomorphic dynamics on tori, Proc. AMS, 144, 7 (2016) 2911-2922.
  3. pdf Co-axial monodromy, Ann. Sc. Norm. Super. Pisa, Cl. di Sci. (5) 20, 2 (2020) 619-634.
  4. pdf Metrics of constant positive curvature with four conic singularities on the sphere, Proc. AMS 148, 9 (2020) 3957-3965.
  5. pdf (with G. Mondello and D. Panov) Moduli of spherical tori with one conical point.

Spherical polygons

  • pdf (with A. Gabrielov and V. Tarasov) Metrics with conic singularities and spherical polygons, Illinois J. Math., 58, 3 (2014) 739-755.
  • pdf (with A. Gabrielov) On metrics of curvature 1 with four singularities on tori and on the sphere, Illinois J. Math., 59, No. 4, 925-947 (2015).
  • pdf (with A. Gabrielov) Spherical rectangles, Arnold Math. J., 2, 4 (2016) 463-486
  • pdf (with A. Gabrielov and V. Tarasov) Spherical quadrilaterals with three non-integer angles, Journal of Math. Ph. Analysis and Geometry, 12 (2016) 2, 134-167.
  • pdf (with A. Gabrielov and V. Tarasov) Metrics with four conic singularities and spherical quadrilaterals, Conformal geometry and Dynamics, 20 (2016) 128--175
  • pdf (with A. Gabrielov) Schwarz--Klein triangles, JMAG. 16, 3 (2020) 263-282.

    Fourier transform

    1. pdf (with D. Novikov) Oscillation of Fourier integrals with a spectral gap, J. de Math. Pures et Appl., 8, 3 (2004), 313-365.

    Analytic continuation of power series

    1. pdf (with A. Atzmon and M. Sodin) Spectral inclusion and analytic continuation, Bull. London Math. Soc., 31 (1999), 722-728.
    2. pdf Fabry's theorem for power series with regularly varying coefficients, PAMS, 136 (2008), 4389-4394.
    3. pdf Densities in Fabry's theorem, Illinois J. Math., 52, (2008) No. 4, 1277-1290.

    Harmonic mappings

    1. pdf (with W. Bergweiler) On the number of solutions of a transcendental equation arising in the theory of gravitational lensing, CMFT, Comput. Methods Funct. Theory 10 (2010), No. 1, 303--324.

    New proofs of important theorems

    1. pdf Meromorphic solutions of algebraic differential equations, Russian Math. Surveys, 37, 4 (1982), 61-95. Correction: 38, 6 (1983).
    2. pdf New proof of Drasin's theorem on meromorphic functions of finite order with maximal deficiency sum I, Function Theory, Functional Analysis and their Application, (1989), 51, 107-116. English translation: Journal of Soviet Math., 52, 6 (1990), 3522-3529.
    3. pdf New proof of Drasin's theorem on meromorphic functions of finite order with maximal deficiency sum II, Function Theory, Functional Analysis and their Application, 52 (1989) 69-77. English translation: Journal of Soviet Math 52, 5 (1990) 3397-3403.
    4. pdf (with D. Hamilton) On the area distortion by quasiconformal mappings, Proc. AMS, 123, 9 (1995), 2793-2797.
    5. pdf A Picard type theorem for holomorphic curves, Periodica Mathematica Hungarica, 38, 1-2 (1999), 39-42.
    6. pdf Elementary proof of the B. and M. Shapiro conjecture for rational functions, in the book: Notions of positivity and the geometry of polynomials, trends in mathematics, Springer, Basel, 2011, p. 167-178.
    7. pdf Herbert Stahl's proof of the BMV conjecture, Mat. Sbornik, 206, 1, (2015) 87-92.
    8. pdf (with W. Bergweiler) Green functions and antiholomorphic dynamics on tori, Proc. AMS, 144, 7 (2016) 2911-2922.
    9. pdf (with A. Fryntov) Stability in the Marcinkiewicz theorem, JMAG 2021.

    History of mathematics

    1. pdf Ahlfors' contribution to the theory of meromorphic functions.
    2. pdf (with I. V. Ostrovskii and M. Sodin) Anatolii Asirovich Goldberg.
    3. pdf Interactions of function theory with holomorphic dynamics.