Research

Constructing Pairs of Pants, Ann. Acad. Sci. Fennicae, Series A. I. Math. 15, 1990, 65-74.

Generalizing the hyperbolic collar lemma, Bulletin of the Amer. Math. Soc., 27, 1, July 1992, 154-158.

Hyperbolic structures for surfaces of infinite type, Trans. Amer. Math. Soc.  336, no. 1, March 1993, 421-444.

The geometry of totally geodesic hypersurfaces in hyperbolic manifolds, Differential geometry: Riemannian geometry (Los Angeles, CA, 1990), 81–87, Proc. Sympos. Pure Math., 54, Part 3, Amer. Math. Soc., Providence, RI, 1993.

The stable neighborhood theorem and lengths of closed geodesics, Proc. of the Amer. Math. Soc., 119, 1, Sept. 1993, 217-224.

The orthogonal spectrum of a hyperbolic manifold, American Journal of Mathematics, 115, 5, Oct. 1993, 1139-1159.

Tubular neighborhoods of totally geodesic hypersurfaces in hyperbolic manifolds, Inventiones Mathematicae, 117, 1994, 207-225. 

Constructing pairs of pants II, Low-dimensional topology (Knoxville, TN, 1992), 15-20, Conf. Proc. Lecture Notes Geom. Topology, III, Internat. Press, Cambridge, MA, 1994.

Metric flows in space forms of nonpositive curvature (With Gerard Walschap), Proc. of the Amer. Math. Soc., 123, 10, Oct. 1995, 3177-3181.

Selected problems in Kleinian groups and hyperbolic geometry, Lipa’s legacy (New York, 1995), 9-15, Contemp. Math., 211, Amer. Math. Soc., Providence, RI, 1997.

Large parameter spaces of quasiconformally distinct hyperbolic structures, Journal D’Analyse Mathematique, 71 (1997), 75-85.

Discrete subroups of complex hyperbolic motions (with Robert Miner) , Inventiones Mathematicae, 131, 1998, 85-136.

Quasiconformal mappings and geodesics in the hyperbolic plane, In the tradition of Ahlfors and Bers (Stony Brook, NY, 1998), 1–4, Contemp. Math., 256, Amer. Math. Soc., Providence, RI, 2000.

Hyperbolic 3-manifolds with nonintersecting closed geodesics, (with Scott Wolpert) Geometriae Dedicata, 97 (2003), 251-257.

Mobius transformations of the circle form a maximal convergence group (with Mahmoud Zeinalian), The geometry of Riemann surfaces and abelian varieties, III Iberoamerican Congress on Geometry, Contemp. Math., 397, Amer. Math. Soc., Providence, RI, 2006.

Maximal convergence groups and rank one symmetric spaces (with Mahmoud Zeinalian), Journal of the Australian Mathematical Society, 83 (1), August 2007.

Geometrically infinite surfaces with discrete length spectra (with Youngju Kim), Geometriae Dedicata, 137 (2008), 219-240.

Space form isometries as commutators and products of involutions (with Bernard Maskit), Trans. Amer. Math. Soc. 364 (2012), no. 9, 5015–5033.

Generating the Mobius group with involution conjugacy classes (with Karan Puri), Proc. Amer. Math. Soc. 140 (2012), no. 11, 4011-4016.

Conformally scattered sets in the unit circle, Quasiconformal mappings, Riemann surfaces, and Teichmuller spaces, 23–29, Contemp. Math., 575, Amer. Math. Soc., Providence, RI, 2012.

Universal length bounds for non-simple closed geodesics on hyperbolic surfaces, Journal of Topology 2013; doi: 10.1112/jtopol/jtt005.

Bers pants decomposition theorem, (with Perry Susskind), Lipman Bers, a life in Mathematics. Edited by Linda Keen, Irwin Kra, and Rubi Rodriguez. Amer. Math. Soc., Providence, R.I. 2015.

Short geodesics on a hyperbolic surface, Recent Advances in Mathematics, Ramanujan Mathematical Society, Lecture Notes Series No. 21, 2015, pp 39-43.

Geometric filling curves on surfaces  (with Hugo Parlier and Juan Souto), Bull. London Math. Soc. 49,  (2017), no. 4, 660-669. 

 Geodesically complete hyperbolic structures, (with Dragomir Saric),  Mathematical Proceedings of the Cambridge Philosophical Society, 166, 2019, no. 2,  219-242.  

Combinatorial growth in the modular group (with Robert Suzzi Valli), Groups, Geometry, and Dynamics, 16 (2022), no. 2, 683-703. 

There are no exotic ladder surfaces (with Nicholas Vlamis), Annales Fennici Mathematici, 47 (2022), no. 2, 1007-1023.

The type problem for Riemann surfaces via Fenchel-Nielsen parameters (with Hrant Hakobyan and Dragomir Saric), Proc. London Math. Soc., (3) 125, (2022), no. 3, 568-625.

Editors' introduction [collection of articles dedicated to Dennis Sullivan] (with Koberda, Thomas, Papadopoulos, Athanase, Seade, Jose, Zeinalian, Mahmoud), EMS Surv. Math. Sci., 9, 2022, 2, 251-274.

Bounded geometry with no bounded pants decomposition (with Hugo Parlier and Nicholas Vlamis), Israel. J. Math. 260,  (2024), no. 1, 235–260. 

The shortest non-simple closed geodesics on a hyperbolic surface (with Hugo Parlier and Hanh Vo), Math. Z., 306 (2024), no. 1, Paper no. 8, 19pp. 

Counting cusp excursions of reciprocal geodesics (with Robert Suzzi Valli), Geometry and Symmetry, Contemp. Math., Amer. Math. Soc., Providence, RI,  Amer. Math. Soc., Providence, RI, Vol 811, 2025.

Prime orthogeodesics, concave cores, and families of identities on hyperbolic surfaces (with Hugo Parlier and Ser Peow Tan), Advances in Mathematics, 460 (2025), Paper No. 11026, 42 pp.

Tubes in complex hyperbolic manifolds (with Youngju Kim), Transactions of the  Amer. Math. Soc.,  378 (2025), no. 3,  pages 2031-2060.

Tubes and Steklov eigenvalues in negatively curved manifolds (with Jade Brisson, Asma Hassannezhad, and Antoine Metras), International Mathematics  Research Notices,  IMRN 2025, no. 3, rnaf001, 25pp. 

Low-lying geodesics on the modular surface and necklaces (with Mingkun Liu), Mathematical research letters, to appear. 

Orthosystoles and orthokissing numbers, (with Federica Fanoni), Algebraic and geometric topology, to appear. 

A Bers type classification of big mapping classes (with Yassin Chandran), submitted.

Counting reciprocal hyperbolic elements in Hecke groups (Blanca Marmolejo and Robert Suzzi Valli), submitted.