PAPERS

Fields of interest

My research interests include Teichmuller spaces (both infinite-dimensional and finite-dimensional), quasiconformal and quasisymmetric maps, hyperbolic geometry in dimensions 2 and 3, and real and complex dynamics.

Editorship

Conformal dynamics and hyperbolic geometry.
Proceedings of the conference in honor of Linda Keen’s 70th birthday held at the Graduate School and University Center of CUNY, New York, October 21–23, 2010. Edited by Francis Bonahon, Robert L. Devaney, Frederick P. Gardiner and Dragomir Šarić. Contemporary Mathematics, 573. American Mathematical Society, Providence, RI, 2012.

Preprints

Ergodicity of the geodesic flow on symmetric surfaces, on Arxiv, to appear in Trans. Amer. Math. Soc. (joint with M. Pandazis).

Circle homeomorphisms with square summable diamond shears, on Arxiv (joint with Y. Wang and C. Wolfram)

Quasisymmetric maps, shears, lambda lengths and flips, on Arxiv (with H. Parlier)

Quadratic differentials and foliations on infinite Riemann surfaces, on Arxiv.

On complex extension of the Liouville map on Arxiv (with X. Dong)

Extremal maps of the universal hyperbolic solenoid on Arxiv (with A. Epstein and V. Markovic)

Published papers

[37] The type problem for Riemann surfaces via Fenchel-Nielsen parameters, Proc. Lond. Math. Soc. (3) 125 (2022), no. 3, 568–625. (joint with A. Basmajian and H. Hakobyan)

[36] The heights theorem for infinite surfaces, Geom. Dedicata 216 (2022), no. 3, Paper No. 33, 23 pp.

[35] Train tracks and measured laminations on infinite surfaces. Trans. Amer. Math. Soc. 374 (2021), no. 12, 8903–8947.

[34] A Thurston boundary and visual sphere of the universal Teichmüller space. J. Anal. Math. 143 (2021), no. 2, 681–721. (with H. Hakobyan)

[33] A Thurston boundary for infinite-dimensional Teichmüller spaces. Math. Ann. 380 (2021), no. 3-4, 1119–1167. (with F. Bonahon)

[32] Shears for quasisymmetric maps. Proc. Amer. Math. Soc. 149 (2021), no. 6, 2487–2499.

[31] Convergence of Teichmüller deformations in the universal Teichmüller space. Proc. Amer. Math. Soc. 147 (2019), no. 11, 4877–4889. (with H. Miyachi)

[30] Geodesically complete hyperbolic structures. Math. Proc. Cambridge Philos. Soc. 166 (2019), no. 2, 219–242. (with A. Basmajian)

[29] Limits of Teichmüller geodesics in the universal Teichmüller space. Proc. Lond. Math. Soc. (3) 116 (2018), no. 6, 1599–1628. (with H. Hakobyan)

[28] Thurston’s boundary for Teichmüller spaces of infinite surfaces: the length spectrum. Proc. Amer. Math. Soc. 146 (2018), no. 6, 2457–2471.

[27] Fenchel-Nielsen coordinates for asymptotically conformal deformations. Ann. Acad. Sci. Fenn. Math. 41 (2016), no. 1, 167–176.

[26] Vertical limits of graph domains. Proc. Amer. Math. Soc. 144 (2016), no. 3, 1223–1234. (with H. Hakobyan)

[25] Fenchel-Nielsen coordinates on upper bounded pants decompositions. Math. Proc. Cambridge Philos. Soc. 158 (2015), no. 3, 385–397.

[24] Earthquakes in the length-spectrum Teichmüller spaces. Proc. Amer. Math. Soc. 143 (2015), no. 4, 1531–1543.

[23] Fenchel-Nielsen coordinates with small imaginary parts. Trans. Amer. Math. Soc. 366 (2014), no. 12, 6541–6565.

[22] Bendings by finitely additive transverse cocycles. J. Topol. 7 (2014), no. 2, 557–588.

[21] Zygmund vector fields, Hilbert transform and Fourier coefficients in shear coordinates. Amer. J. Math. 135 (2013), no. 6, 1559–1600.

[20] Uniform weak∗ topology and earthquakes in the hyperbolic plane. Proc. Lond. Math. Soc. (3) 105 (2012), no. 6, 1123–1148. (with H. Miyachi) *Note: see journal version for the latest

[19] Elementary moves and the modular group of the compact solenoid. Conformal dynamics and hyperbolic geometry, 11–33, Contemp. Math., 573, Amer. Math. Soc., Providence, RI, 2012. (with R. Chamanara)

[18] Infinitesimal Liouville currents, cross-ratios and intersection numbers. J. Topol. 5 (2012), no. 1, 213–225. (with F. Bonahon)

[17] Circle homeomorphisms and shears. Geom. Topol. 14 (2010), no. 4, 2405–2430.

[16] Some remarks on bounded earthquakes. Proc. Amer. Math. Soc. 138 (2010), no. 3, 871–879.

[15] The universal properties of Teichmüller spaces. Surveys in differential geometry. Vol. XIV. Geometry of Riemann surfaces and their moduli spaces, 261–294, Surv. Differ. Geom., 14, Int. Press, Somerville, MA, 2009. (with V. Markovic)

[14] The Teichmüller theory of the solenoid. Handbook of Teichmüller theory. Vol. II, 811–857, IRMA Lect. Math. Theor. Phys., 13, Eur. Math. Soc., Zürich, 2009.

[13] The Teichmüller distance between finite index subgroups of PSL2(ℤ). Geom. Dedicata 136 (2008), 145–165. (with V. Markovic)

[12] On quasiconformal deformations of the universal hyperbolic solenoid. J. Anal. Math. 105 (2008), 303–343.

[11] Teichmüller theory of the punctured solenoid. Geom. Dedicata 132 (2008), 179–212.

[10] Bounded earthquakes. Proc. Amer. Math. Soc. 136 (2008), no. 3, 889–897.

[9] Earthquakes and Thurston’s boundary for the Teichmüller space of the universal hyperbolic solenoid. Pacific J. Math. 233 (2007), no. 1, 205–228.

[8] A presentation for the baseleaf preserving mapping class group of the punctured solenoid. Algebr. Geom. Topol. 7 (2007), 1171–1199. (with S. Bonnot and R. Penner)

[7] Teichmüller mapping class group of the universal hyperbolic solenoid. Trans. Amer. Math. Soc. 358 (2006), no. 6, 2637–2650. (with V. Markovic)

[6] Real and complex earthquakes. Trans. Amer. Math. Soc. 358 (2006), no. 1, 233–249.

[5] Geodesic currents and Teichmüller space. Topology 44 (2005), no. 1, 99–130.

[4] Infinitesimal Liouville distributions for Teichmüller space. Proc. London Math. Soc. (3) 88 (2004), no. 2, 436–454.

[3] Barycentric extension and the Bers embedding for asymptotic Teichmüller space. Complex manifolds and hyperbolic geometry (Guanajuato, 2001), 87–105, Contemp. Math., 311, Amer. Math. Soc., Providence, RI, 2002. (C. Earle and V. Markovic)

[2] Extremal metrics and modulus. Czechoslovak Math. J. 52(127) (2002), no. 2, 225–235. (with I. Anic and M. Mateljevic)

[1] Complex earthquakes are holomorphic. Thesis (Ph.D.)–City University of New York. 2001.