On the index of minimal 2-tori in the 4-sphere, J. Reine Angew. Math. 8?? (202?) (in press, see also DOI: https://doi.org/10.1515/crelle-2023-0066 or arXiv:1803.01615 – with P. Wang)
A Gordian Pair of Links, Geometriae Dedicata 217 (2023) Article 47 (see also DOI: https://doi.org/10.1007/s10711-023-00783-1 or arXiv:1908.05610 – with W. Kusner)
On the Canham Problem: Bending Energy Minimizers for any Genus and Isoperimetric Ratio, Arch. Rat. Mech. Anal. 247 (2023) Article 10 (see also DOI: https://doi.org/10.1007/s00205-022-01833-w or arXiv:2104.10045 – with P. McGrath)
On Steklov Eigenspaces for Free Boundary Minimal Surfaces in the Unit Ball, Amer. J. Math. 14? (202?) ???-??? (in press, see also arXiv:2011.06884 for an earlier version – with P. McGrath)
Numerical methods for biomembranes: Conforming subdivision methods versus non-conforming PL methods, Math. Comp. 90:328 (2021) 471-516 (see also DOI: https://doi.org/10.1090/mcom/3584 – with P. Brogan, J. Chen, Y. Yang, T. Yu & A. Zigerelli)
The Mathematics of Richard Schoen, Notices Amer. Math. Soc. 65:11 (2018) 1349-1376 (see also DOI: http://dx.doi.org/10.1090/noti1749 - with H. Bray, M. Eichmair, A. Fraser, L.H. Huang, F.C. Marques, C. Mese, W. Minicozzi, K. Uhlenbeck & S.T. Yau)
Configuration Spaces of Equal Spheres Touching a Given Sphere: The Twelve Spheres Problem, Bolyai Soc. Math. Study 27 (2018) 219-278 (New Trends in Intuitive Geometry – the Laszlo Fejes Toth Centenary volume; see also arXiv:1611.10297 v3 - with W. Kusner, J. Lagarias & S.Shlosman)
Willmore Bending Energy on the Space of Surfaces, MSRI Emissary (2016) 1 & 5-8 (see https://www.msri.org/system/cms/files/204/files/original/Emissary-2016-S... – with A. Mondino & F. Schulze)
The expected total curvature of random polygons, Amer. J. Math. 137 (2015), 411-438 (with J. Cantarella, A.Y. Grosberg & C. Shonkwiler)
Ropelength Criticality, Geometry & Topology 18 (2014) 1973-2043 (with J. Cantarella, J. Fu & J. Sullivan)
Topological Colloids, Nature 493 (2013) 200-205 (with R. Kamien, T. Lubensky, I. Smalyukh & al.)
There is no triangulation of the torus with vertex degrees 5, 6, . . . , 6, 7 and related results: Geometric proofs for combinatorial theorems, Geometriae Dedicata 166 (2013) 15-29 (with I. Ismestiev, G. Rote, B. Springborn & J. Sullivan)
Coplanar k-Unduloids Are Nondegenerate, Int. Math. Res. Notices (2009) 3391-3416 (with K.G. Brauckmann, N. Korevaar, J. Ratzkin & J. Sullivan)
Coplanar constant mean curvature surfaces, Comm. Anal. Geom. 15 (2007) 985-1023 (with K.G. Brauckmann & J. Sullivan)
Criticality for the Gehring Link Problem, Geometry & Topology 10 (2006) 2045-2105 (with J. Cantarella, J. Fu, J. Sullivan & N. Wrinkle)
On the nondegeneracy of constant mean curvature surfaces, Geom. and Funct. Analysis 16 (2006) 891-923 (with N. Korevaar & J. Ratzkin)
Conformal structures and necksizes of embedded constant mean curvature surfaces, Global theory of minimal surfaces, 585-596, Clay Math. Proc. 2 Amer. Math. Soc., Providence, RI, 2005
Topology, Geometry and Conformal Structure of Properly Embedded Minimal Surfaces, J. Differential Geom. 67 (2004) 377-393 (with P. Collin, W. Meeks & H. Rosenberg)
The second hull of a knotted curve, Amer. J. Math. 125 (2003) 1335–1348. (with J. Cantarella, G. Kuperberg & J. Sullivan)
Embedded CMC Surfaces of genus zero and three ends, J. Reine Angew. Math. 564 (2003) 35-61 (with K.G. Brauckmann & J. Sullivan)
On the Minimum Ropelength of Knots and Links, Inventiones Math. 150 (2002) 257-286 (with J. Cantarella & J. Sullivan)
Constant Mean Curvature Surfaces with Three Ends, Proc. Nat. Acad. Sci. (USA) 97 (2000) 14067-14068 (with K.G. Brauckmann & J. Sullivan)
Tight knot values deviate from linear relations, Nature 392 (1998) 237-238 (with J. Cantarella & J. Sullivan)
The Spinor Representation of Surfaces in Space, arXiv:dg-ga/9610005 (1996) 37 pages plus appendices (with N. Schmitt)
The Moduli Space of Complete Embedded Constant Mean Curvature Surfaces, Geom. and Funct. Analysis 6 (1996) 120-137 (with R. Mazzeo & D. Pollack)
The Global Structure of Constant Mean Curvature Surfaces, Inventiones Math. 114 (1993) 311-332 (with N. Korevaar)
Torus knots extremizing the Mobius energy, Experiment. Math. 2 (1993), no. 1, 1-9 (with Denise Kim)
The number of faces in a minimal foam, Proc. Roy. Soc. London, Ser. A 439 (1992), no. 1907, 683-686
Minimizing the squared mean curvature integral for surfaces in space forms. Experiment. Math. 1 (1992), no. 3, 191–207 (with L. Hsu & J. Sullivan)
Constant mean curvature surfaces in hyperbolic space, Amer. J. Math. 114 (1992), 1-43 (with N. Korevaar, W. Meeks & B. Solomon)
Bubbles, conservation laws, and balanced diagrams, Geometric analysis and computer graphics (Berkeley, CA, 1988) 103-108, Math. Sci. Res. Inst. Publ. 17 Springer, New York, 1991
The Structure of Complete Embedded Surfaces with Constant Mean Curvature, J. Differential Geom. 30 (1989) 465-503 (with N. Korevaar & B. Solomon)
Comparison Surfaces for the Willmore Problem, Pacific J. Math. 138 (1989) 317-345
Conformal Geometry and Complete Minimal Surfaces, Bull. Amer. Math. Soc. 17 (1987) 291-295
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