53. Self-intersections of Laurent polynomials and the density of Jordan curves (with Sergei Kalmykov), Proc. Amer. Math. Soc., to appear.
Preprint
52. Optimal extension of Lipschitz embeddings in the plane, Bull. London Math. Soc., to appear.
Journal Preprint
51. Fourier series of circle embeddings (with Xuerui Yang), Comput. Methods Funct. Theory 19 (2019), no. 2, 323-340.
Journal Preprint
50. Removable sets for intrinsic metric and for holomorphic functions (with Sergei Kalmykov and Tapio Rajala), J. Anal. Math., to appear.
Preprint
49. Symmetrization and extension of planar bi-Lipschitz maps, Ann. Acad. Sci. Fenn. Math. 43 (2018), no. 1, 541-556.
Journal Preprint
48. Uniform convergence of Green’s functions (with Sergei Kalmykov), Complex Var. Elliptic Equ. 64 (2019), no. 4, 557-562.
Journal Preprint
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 pdf Preprint
46. Lipschitz retractions in Hadamard spaces via gradient flow semigroups (with Miroslav Bačák), Canad. Math. Bull. 59 (2016), no. 4, 673–681.
Journal Preprint
45. Conformal contractions and lower bounds on the density of harmonic measure, Potential Analysis 46 (2017), no. 2, 385-391.
Journal Preprint
44. Lipschitz retraction of finite subsets of Hilbert spaces, Bull. Aust. Math. Soc. 93 (2016), no. 1, 146-151.
Journal Preprint
43. Bi-Lipschitz embedding of projective metrics, Conform. Geom. Dyn. 18 (2014), 110-118.
Journal Preprint
42. Symmetric products of the line: embeddings and retractions, Proc. Amer. Math. Soc. 143 (2015), 801-809.
Journal Preprint
41. Sharp distortion growth for bilipschitz extension of planar maps, Conform. Geom. Dyn. 16 (2012), 124-131.
Journal Preprint
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
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
38. Quasisymmetric graphs and Zygmund functions (with Jani Onninen), J. Anal. Math. 118 (2012), no. 1, 343-361.
Journal Preprint
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
36. Harmonic mapping problem in the plane (with Jani Onninen), J. Anal. 18 (2010), 279–295.
Journal
35. Diffeomorphic approximation of Sobolev homeomorphisms (with Tadeusz Iwaniec and Jani Onninen), Arch. Rat. Mech. Anal. 201 (2011), no. 3, 1047–1067.
Journal Preprint
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
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
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
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
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
29. The Nitsche conjecture (with Tadeusz Iwaniec and Jani Onninen), J. Amer. Math. Soc. 24 (2011), no. 2, 345–373.
Journal Preprint
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
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 Preprint
26. An N-dimensional version of the Beurling-Ahlfors extension (with Jani Onninen), Ann. Acad. Sci. Fenn. Math. 36 (2011), 321–329.
Journal Preprint
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
24. Variation of quasiconformal mappings on lines (with Jani Onninen), Studia Math. 195 (2009), no. 3, 257–274.
Journal Preprint
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
22. Dynamics of quasiconformal fields (with Tadeusz Iwaniec and Jani Onninen), J. Dynam. Differential Equations 23 (2011), no. 1, 185–212.
Journal Preprint
21. On injectivity of quasiregular mappings (with Tadeusz Iwaniec and Jani Onninen), Proc. Amer. Math. Soc. 137 (2009), no. 5, 1783–1791.
Journal Preprint
20. A geometric approach to accretivity, Studia Math. 181 (2007), no. 1, 87–100.
Journal
19. Doubling measures, monotonicity, and quasiconformality (with Diego Maldonado and Jang-Mei Wu), Math. Z. 257 (2007), no. 3, 525–545.
Journal Preprint
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
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
16. Quasiconformal geometry of monotone mappings, J. London Math. Soc. 75 (2007), no. 2, 391–408.
Journal
15. Conformal dimension does not assume values between zero and one, Duke Math. J. 134 (2006), no. 1, 1–13.
Journal
14. Mappings with convex potentials and the quasiconformal Jacobian problem (with Diego Maldonado), Illinois J. Math. 49 (2005), no. 4, 1039–1060.
Journal
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
12. Comparison theorems for the one-dimensional Schrödinger equation, Ark. Mat. 43 (2005), no. 2, 403–418.
Journal
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
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.
9. Hölder spaces of quasiconformal mappings, Publ. Inst. Math. (Beograd) 75 (89) (2004), 87–94.
Journal
8. Quasiregular mappings of maximal local modulus of continuity, Ann. Acad. Sci. Fenn. Math. 29 (2004), 211–222.
Journal
7. Boundary values of mappings of finite distortion (with Jani Onninen), Rep. Univ. Jyväskylä Dep. Math. Stat. 92 (2003), 175–182.
Preprint
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.
In Russian In English
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.
In Russian In English
4. Domains with convex hyperbolic radius, Acta Math. Univ. Comenianae 70 (2001), no. 2, 207–213.
Journal
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.
In Russian In English
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
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