Research interests: geometric mapping theory (quasiconformal, conformal, harmonic, Sobolev, bi-Lipschitz maps), analysis and geometry of metric spaces, geometric variational problems, potential theory, complex analysis.
Academic profiles: arXiv, Google Scholar, MathSciNet.
Papers and preprints:
63. A sharp bound on the number of self-intersections of a trigonometric curve (with Sergei Kalmykov), J. Math. Anal. Appl. 543 (2025), no. 2, 128995. Journal Preprint
62. Anti-absorbing ternary operations on metric spaces, Topology Appl. 360 (2025), 109153. Journal Preprint
61. Lipschitz means and mixers on metric spaces, Illinois J. Math. 68 (2024), no. 1, 167-187. Journal Preprint MathSciNet
60. Lipschitz clustering in metric spaces, J. Geom. Anal. 32 (2022), no. 7, 188. Journal Preprint MathSciNet
59. Continuity of logarithmic capacity (with Sergei Kalmykov), J. Math. Anal. Appl. 505 (2022), no. 1, 125585. Journal Preprint MathSciNet
58. Extreme values of the derivative of Blaschke products and hypergeometric polynomials (with Xuerui Yang), Bull. Sci. Math. 169 (2021), 102979. Journal Preprint MathSciNet
57. Growth rate of Lipschitz constants for retractions between finite subset spaces (with Earnest Akofor), Studia Math. 260 (2021), no. 3, 317-326. Journal Preprint MathSciNet
56. Circle embeddings with restrictions on Fourier coefficients (with Liulan Li), J. Math. Anal. Appl. 488 (2020), no. 2, 124083. Journal Preprint MathSciNet
55. Near-isometric duality of Hardy norms with applications to harmonic mappings (with Xuerui Yang), J. Math. Anal. Appl. 487 (2020), no. 2, 124040. Journal Preprint MathSciNet
54. Algebraic structure of the range of a trigonometric polynomial (with Xuerui Yang), Bull. Aust. Math. Soc. 102 (2020), no. 2, 251-260. Journal Preprint MathSciNet
53. Self-intersections of Laurent polynomials and the density of Jordan curves (with Sergei Kalmykov), Proc. Amer. Math. Soc. 151 (2023), no. 2, 547-554. Journal Preprint MathSciNet
52. Optimal extension of Lipschitz embeddings in the plane, Bull. London Math. Soc. 51 (2019), no. 4, 622-632. Journal Preprint MathSciNet
51. Fourier series of circle embeddings (with Xuerui Yang), Comput. Methods Funct. Theory 19 (2019), no. 2, 323-340. Journal Preprint MathSciNet
50. Removable sets for intrinsic metric and for holomorphic functions (with Sergei Kalmykov and Tapio Rajala), J. Anal. Math. 139 (2019), no. 2, 751-772. Journal Preprint MathSciNet
49. Symmetrization and extension of planar bi-Lipschitz maps, Ann. Acad. Sci. Fenn. Math. 43 (2018), no. 1, 541-556. Journal Preprint MathSciNet
48. Uniform convergence of Green's functions (with Sergei Kalmykov), Complex Var. Elliptic Equ. 64 (2019), no. 4, 557-562. Journal Preprint MathSciNet
47. On the existence of harmonic mappings between doubly connected domains (with Liulan Li), Proc. Roy. Soc. Edinburgh Sect. A 148 (2018), no. 3, 619-628. Journal Preprint MathSciNet
46. Lipschitz retractions in Hadamard spaces via gradient flow semigroups (with Miroslav Bačák), Canad. Math. Bull. 59 (2016), no. 4, 673-681. Journal Preprint MathSciNet
45. Conformal contractions and lower bounds on the density of harmonic measure, Potential Analysis 46 (2017), no. 2, 385-391. Journal Preprint MathSciNet
44. Lipschitz retraction of finite subsets of Hilbert spaces, Bull. Aust. Math. Soc. 93 (2016), no. 1, 146-151. Journal Preprint MathSciNet
43. Bi-Lipschitz embedding of projective metrics, Conform. Geom. Dyn. 18 (2014), 110-118. Journal Preprint MathSciNet
42. Symmetric products of the line: embeddings and retractions, Proc. Amer. Math. Soc. 143 (2015), 801-809. Journal Preprint MathSciNet
41. Sharp distortion growth for bilipschitz extension of planar maps, Conform. Geom. Dyn. 16 (2012), 124-131. Journal Preprint MathSciNet
Note: The proof of inequality (3.3) contains a slight mistake, but the inequality itself is true. In order to correct the proof, one should replace "Let ρ = dist(ζ, Γj)" at the bottom of page 126 with "Let ρ = dist(ζ, Γ1) - |ζ|". Then the statement "∂Ω ∩ B(0, ρ) is disjoint from Γ1" is true, and the rest proceeds as written, including the inequality (ρ − |ζ|)/(ρ + |ζ|) ≤ sin(3π/8). Solve this inequality for ρ to get ρ ≤ 29|ζ|, hence dist(ζ, Γ1) ≤ 30|ζ| as is claimed in (3.3).
40. Lipschitz regularity for inner-variational equations (with Tadeusz Iwaniec and Jani Onninen), Duke Math. J. 162 (2013), no. 4, 643-672. Journal Preprint MathSciNet
39. Approximation up to the boundary of homeomorphisms of finite Dirichlet energy (with Tadeusz Iwaniec and Jani Onninen), Bull. London Math. Soc. 44 (2012), no. 5, 871-881. Journal Preprint MathSciNet
38. Quasisymmetric graphs and Zygmund functions (with Jani Onninen), J. Anal. Math. 118 (2012), no. 1, 343-361. Journal Preprint MathSciNet
37. The Hopf-Laplace equation: harmonicity and regularity (with Jan Cristina, Tadeusz Iwaniec, and Jani Onninen), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13 (2014), no. 4, 1145-1187. Journal Preprint MathSciNet
36. Harmonic mapping problem in the plane (with Jani Onninen), J. Anal. 18 (2010), 279-295. Journal MathSciNet
35. Diffeomorphic approximation of Sobolev homeomorphisms (with Tadeusz Iwaniec and Jani Onninen), Arch. Rat. Mech. Anal. 201 (2011), no. 3, 1047-1067. Journal Preprint MathSciNet
34. Existence of energy-minimal diffeomorphisms between doubly connected domains (with Tadeusz Iwaniec, Ngin-Tee Koh, and Jani Onninen), Invent. Math. 186 (2011), no. 3, 667-707. Journal Preprint MathSciNet
33. Hopf differentials and smoothing Sobolev homeomorphisms (with Tadeusz Iwaniec and Jani Onninen), Int. Math. Res. Not. IMRN 2012 (2012), no. 14, 3256-3277. Journal Preprint MathSciNet
32. The harmonic mapping problem and affine capacity (with Tadeusz Iwaniec and Jani Onninen), Proc. Roy. Soc. Edinburgh Sect. A 141 (2011), no. 5, 1017-1030. Journal Preprint MathSciNet
Note: A part of the proof of Theorem 1.5, namely Case 1 in section 4.3, misses the possibility that the domain is the complement of the union of a line segment with two half-lines, all lying on the same line. Such a domain ("double Teichmüller ring") can be treated similarly to the ordinary Teichmüller ring; no new ideas are required. The missing details were later supplied in paper #47 listed above.
31. Doubly connected minimal surfaces and extremal harmonic mappings (with Tadeusz Iwaniec and Jani Onninen), J. Geom. Anal. 22 (2012), no. 3, 726-762. Journal Preprint MathSciNet
30. Area contraction for harmonic automorphisms of the disk (with Ngin-Tee Koh), Bull. London Math. Soc. 43 (2011), no. 1, 91-96. Journal Preprint MathSciNet
29. The Nitsche conjecture (with Tadeusz Iwaniec and Jani Onninen), J. Amer. Math. Soc. 24 (2011), no. 2, 345-373. Journal Preprint MathSciNet
28. Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames (with Julien Giol, David Larson, Nga Nguyen, and James Tener), Operators and Matrices 5 (2011), no. 1, 139-155. Journal Preprint MathSciNet
27. Invertibility of Sobolev mappings under minimal hypotheses (with Jani Onninen and Kai Rajala), Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 2, 517-528. Journal MathSciNet
26. An N-dimensional version of the Beurling-Ahlfors extension (with Jani Onninen), Ann. Acad. Sci. Fenn. Math. 36 (2011), 321-329. Journal Preprint MathSciNet
25. Harmonic mappings of an annulus, Nitsche conjecture and its generalizations (with Tadeusz Iwaniec and Jani Onninen), Amer. J. Math. 132 (2010), no. 5, 1397-1428. Journal Preprint MathSciNet
24. Variation of quasiconformal mappings on lines (with Jani Onninen), Studia Math. 195 (2009), no. 3, 257-274. Journal Preprint MathSciNet
Note: A result similar to Proposition 2.1 was proved by Robert Kaufman in Sobolev spaces, dimension, and random series, Proc. Amer. Math. Soc. 128 (2000), no. 2, 427-431.
23. On invertibility of Sobolev mappings (with Jani Onninen), J. Reine Angew. Math. 2011 (2011), no. 656, 1-16. Journal Preprint MathSciNet
22. Dynamics of quasiconformal fields (with Tadeusz Iwaniec and Jani Onninen), J. Dynam. Differential Equations 23 (2011), no. 1, 185-212. Journal Preprint MathSciNet
21. On injectivity of quasiregular mappings (with Tadeusz Iwaniec and Jani Onninen), Proc. Amer. Math. Soc. 137 (2009), no. 5, 1783-1791. Journal Preprint MathSciNet
20. A geometric approach to accretivity, Studia Math. 181 (2007), no. 1, 87-100. Journal MathSciNet
19. Doubling measures, monotonicity, and quasiconformality (with Diego Maldonado and Jang-Mei Wu), Math. Z. 257 (2007), no. 3, 525-545. Journal Preprint MathSciNet
18. Convex functions and quasiconformal mappings (with Diego Maldonado), in Harmonic analysis, partial differential equations, and related topics, 93-104, Contemporary Math., vol. 428, Amer. Math. Soc., 2007. Proceedings Preprint MathSciNet
17. Hyperbolic and quasisymmetric structure of hyperspaces (with Jeremy Tyson), in In the tradition of Ahlfors-Bers, IV, 151-166, Contemporary Math., vol. 432, Amer. Math. Soc., 2007. Proceedings Preprint MathSciNet
16. Quasiconformal geometry of monotone mappings, J. London Math. Soc. 75 (2007), no. 2, 391-408. Journal MathSciNet
15. Conformal dimension does not assume values between zero and one, Duke Math. J. 134 (2006), no. 1, 1-13. Journal MathSciNet
14. Mappings with convex potentials and the quasiconformal Jacobian problem (with Diego Maldonado), Illinois J. Math. 49 (2005), no. 4, 1039-1060. Journal MathSciNet
13. On Hölder regularity for elliptic equations of non-divergence type in the plane (with Albert Baernstein), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2005), 295-317. Journal Preprint MathSciNet
12. Comparison theorems for the one-dimensional Schrödinger equation, Ark. Mat. 43 (2005), no. 2, 403-418. Journal MathSciNet
11. Quasiregular gradient mappings and strong solutions of elliptic equations (with David Opěla), in The p-harmonic equation and recent advances in analysis, 145-157, Contemporary Math. vol. 370, AMS, 2005. Proceedings Preprint MathSciNet
10. On G-compactness of the Beltrami operators (with Flavia Giannetti, Tadeusz Iwaniec, Gioconda Moscariello, and Carlo Sbordone), in Nonlinear homogenization and its applications to composites, polycrystals and smart materials, 107-138, NATO Science Series II, vol. 170, Kluwer, 2004. MathSciNet
9. Hölder spaces of quasiconformal mappings, Publ. Inst. Math. (Beograd) 75 (89) (2004), 87-94. Journal MathSciNet
8. Quasiregular mappings of maximal local modulus of continuity, Ann. Acad. Sci. Fenn. Math. 29 (2004), 211-222. Journal MathSciNet
7. Boundary values of mappings of finite distortion (with Jani Onninen), Rep. Univ. Jyväskylä Dep. Math. Stat. 92 (2003), 175-182. Preprint MathSciNet
6. Monotonicity of the generalized reduced modulus, J. Math. Sci., New York 118 (2003), no.1, 4861-4870; translation from Zap. Nauchn. Sem. S-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 276 (2001), Anal. Teor. Chisel i Teor. Funkts. 17, 219-236. Journal MathSciNet
5. Estimates of conformal radius and distortion theorems for univalent functions, J. Math. Sci., New York 110 (2002), no. 6, 3111-3120; translation from Zap. Nauchn. Sem. S-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 263 (2000), Anal. Teor. Chisel i Teor. Funkts. 16, 141-156. Journal MathSciNet
4. Domains with convex hyperbolic radius, Acta Math. Univ. Comenianae 70 (2001), no. 2, 207-213. Journal MathSciNet
3. The reduced modulus of the complex sphere (with Vladimir Dubinin), J. Math. Sci., New York 105 (2001), no. 4, 2165-2179; translation from Zap. Nauchn. Sem. S-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 254 (1998), Anal. Teor. Chisel i Teor. Funkts. 15, 76-94. Journal MathSciNet
2. On the inner radii of symmetric nonoverlapping domains, Russian Math. (Iz. VUZ) 44 (2000), no. 6, 77-78; translation from Izv. Vyssh. Uchebn. Zaved. Mat. (2000), no. 6, 80-81. PDF file MathSciNet
1. On the problem of extremal partitioning with free poles on the circle, Dal'nevost. Mat. Sb. 2 (1996), 96-98. (In Russian). PDF file MathSciNet