Selected Papers

3-Manifolds

• Acylindrical surfaces in 3-manifolds Michigan Math. J. 42 (1995) 357-365.
• Bounded 3-manifolds admit negatively curved metrics with concave boundary J. Differential Geometry 40, (1994) 449-459.
• Stabilization of Heegaard splittings, , Geometry & Topology 13 (2009) 2029-2050 (with A.Thompson and W.P. Thurston).
• Acylindrical.pdf
• Boundary-slopes of immersed surfaces in 3-manifolds, J. Differential Geometry 52 (1999) 303-325 (with H. Rubinstein and S. Wang).
• Configurations of curves on surfaces Proc. of the KirbyFest, Geometry and Topology Monographs, Volume 2, J. Hass and M. Scharlemann Ed., (1999) 201-213 (with P. Scott).
• , Knots and k-width , Geometriae Dedicata, 143, (2009) 7--18 (with J.H. Rubinstein and A. Thompson).
• What is an Almost Normal Surface Proceedings of Geometry and Topology Down Under: The Rubinstein birthday conference. Contemporary Mathematics 597 (2013), 1-14.
• On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds , Proc. Amer. Math. Soc. 130 (2002), 1851-1857 (with S. Wang and Q. Zhou).
• Compactifying Covering spaces of 3-manifolds, Bull. Amer. Math. Soc. 16 (1987) 117-119 (with J.H. Rubinstein and G. P. Scott).
• Acylindrical.pdf
• Simple closed geodesics in hyperbolic 3-manifolds, Bull. London Math. Soc. 31 (1999) 81-86 (with 37. C. Adams and G. P. Scott)
• Homotopy equivalence and homeomorphism of 3-manifolds Topology 31, (1992) 493-517 (with P. Scott).
• Topological and physical knot theory are distinct to appear in Pacific Math. J. (with A. Coward).

Minimal Surfaces

• One-sided closed geodesics on surfaces Mich. Math. J. 33 (1986) 155-168 (with H. Rubinstein).
• Minimal surfaces and the topology of 3-manifolds Global theory of minimal surfaces, Clay Math. Proc., 2, Amer. Math. Soc., Providence, RI, (2005) 705--724,
• The double bubble conjecture ERA-AMS 1, (1995) 98-102 (with M. Hutchings and R. Schlafly).
• Double Bubbles Minimize Annals of Mathematics 151, (2000) 459-515 (with R. Schlafly)
• Intersections of least area surfaces Pacific J. of Math. 152, (1992) 119-123.
• Complete area minimizing surfaces which are not totally geodesic Pacific J. of Math. 111 (1984) 35-38.
• Shortening curves on surfaces Topology 33, (1994) 25-43 (with P. Scott).
• Closed geodesics on surfaces Bull. London Math. Soc. 14 (1982) 385-391. (with M. Freedman and G. P. Scott).
• Least area incompressible surfaces in 3-manifolds Invent. Math. 71 (1983) 609-642 (with M. Freedman and G. P. Scott).
• Acylindrical.pdf
• Geodesic nets on the 2-sphere Proc. Amer. Math. Soc. 124 (1996) 3843-3850 (with F. Morgan).
• Minimal spheres of arbitrarily high Morse index Communications in Analysis and Geometry 11, (2003) 425-439 (with P. Norbury, and J.H. Rubinstein).
• Minimal surfaces in Seifert fiber spaces Topology and its Applications 18 (1984) 145-151.

Complexity

• The minimal number of triangles needed to span a polygon embedded in Rd Discrete and computational geometry, 509-526, Algorithms Combin., 25, Springer, Berlin, 2003 (with J. C. Lagarias).
• Algorithms for knots and 3-manifolds Chaos, Solitons and Fractals 9, (1998) 569-581.
• The computational complexity of knot and link problems Journal of the ACM, 46, (1999) 185-211, (with J. Lagarias and N. Pippenger).
• Unknot Diagrams Requiring a Quadratic Number of Reidemeister Moves to Untangle Discrete & Computational Geometry: 44 (2010), 91-95 (with T. Nowik).
• 3-manifold knot genus is NP-complete STOC 2002 761-766
• The Computational Complexity of Knot Genus and Spanning Area Trans. A.M.S 358, 3821-3850 (2005) (with I Agol and W. P. Thurston).
• The size of spinning disks for polygonal knots Discrete and Computational Geometry 29 (2003) 1-17 (with J.Snoeyink and W.P. Thurston).
• Invariants of knot diagrams Math. Ann. 342 (2008) 125-137 (with T. Nowik) .
• The number of Reidemeister moves needed for unknotting J. Amer. Math. Soc. 14 (2001), no. 2, 399-428 (with J. Lagarias).

Geometric Design

• Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions Journal of Computational #and Applied Mathematics 209, 246-266 (2007) (with R. Farouki).
• Linear perturbation methods for topologically consistent representations of free-form surface intersections Comput. Aided Geom. Design 21 (2004), no. 3, 303-319 (with X. Song, T. Sederberg, J. Zheng, R. Farouki).
• Boundary evaluation algorithms for Minkowski combinations of complex sets using topological analysis of implicit curves Numer. Algorithms 40 (2005), 251-283 (with R. Farouki and C. Y. Han).
• Acylindrical.pdf
• Acylindrical.pdf
• Topologically consistent trimmed surface approximations based on triangular patches Computer Aided Geometric Design 21, 459-478 (2004) (with R. Farouki, C. Y. Han and T. W. Sederberg).
• Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme Advances in Computational Mathematics, 27 (2007), 1--26. (with R. Farouki C. Y. Han, X. Song and T. W. Sederberg).

Geometrical Biology

• Acylindrical.pdf
• Sampling the conformation of protein surface residues for flexible protein docking BMC Bioinform 11 (2010) 575-588 (with P. Francis-Lyon, S. Gu, N Amenta and P. Koehl).
• Globally Optimal Cortical Surface Matching With Exact Landmark Correspondence (with Alex Tsui, Devin Fenton, Phong Vuong, Patrice Koehl, Nina Amenta, David Coeurjolly, Charles DeCarli, and Owen Carmichael), Proceedings Information Processing in Medical Imaging, IPMI 2013, 487-498, 2013.
• Surface-histogram: A new shape descriptor for protein-protein docking Proteins: Structure, Function, and Bioinformatics 80, 221-238, (2012) (with S. Gu, P. Koehl and N. Amenta).