Volume 18, issue 4 (2014)

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Ropelength criticality

Jason Cantarella, Joseph H G Fu, Robert B Kusner and John M Sullivan

Geometry & Topology 18 (2014) 2595–2665
Bibliography
1 T Ashton, J Cantarella, A fast octree-based algorithm for computing ropelength, from: "Physical and numerical models in knot theory" (editors J A Calvo, K C Millett, E J Rawdon, A Stasiak), Ser. Knots Everything 36, World Sci. Publ., Singapore (2005) 323 MR2197947
2 N Bourbaki, Éléments de mathématique: Fonctions d'une variable réelle, Théorie élémentaire, Hermann, Paris (1976) MR0580296
3 J Cantarella, J Ellis, J H G Fu, M Mastin, Symmetric criticality for tight knots, arXiv:1208.3879
4 J Cantarella, J H G Fu, R B Kusner, J M Sullivan, N C Wrinkle, Criticality for the Gehring link problem, Geom. Topol. 10 (2006) 2055 MR2284052
5 J Cantarella, R B Kusner, J M Sullivan, On the minimum ropelength of knots and links, Invent. Math. 150 (2002) 257 MR1933586
6 S S Chern, Curves and surfaces in Euclidean space, from: "Studies in Global Geometry and Analysis" (editor S S Chern), Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.) (1967) 16 MR0212744
7 F H Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975) 247 MR0367131
8 A Coward, J Hass, Topological and physical knot theory are distinct, to appear in Pacific J. Math. arXiv:1203.4019
9 E Denne, Y Diao, J M Sullivan, Quadrisecants give new lower bounds for the ropelength of a knot, Geom. Topol. 10 (2006) 1 MR2207788
10 J J Duistermaat, J A C Kolk, Distributions, Cornerstones, Birkhäuser (2010) MR2680692
11 O C Durumeric, Local structure of ideal knots, II: Constant curvature case, J. Knot Theory Ramifications 18 (2009) 1525 MR2589231
12 H Federer, Curvature measures, Trans. Amer. Math. Soc. 93 (1959) 418 MR0110078
13 A Forsgren, P E Gill, M H Wright, Interior methods for nonlinear optimization, SIAM Rev. 44 (2002) 525 MR1980444
14 O Gonzalez, J H Maddocks, Global curvature, thickness, and the ideal shapes of knots, Proc. Natl. Acad. Sci. USA 96 (1999) 4769 MR1692638
15 D G Luenberger, Optimization by vector space methods, Wiley (1969) MR0238472
16 J H Maddocks, J B Keller, Ropes in equilibrium, SIAM J. Appl. Math. 47 (1987) 1185 MR916236
17 P Pieranski, S Przybyl, High resolution portrait of the ideal trefoil knot, arXiv:1402.5760
18 H L Royden, Real analysis, Macmillan (1988) MR1013117
19 F Schuricht, H von der Mosel, Characterization of ideal knots, Calc. Var. Partial Differential Equations 19 (2004) 281 MR2033143
20 E L Starostin, A constructive approach to modelling the tight shapes of some linked structures, Forma 18 (2003) 263 MR2040086
21 P Strzelecki, M Szumańska, H von der Mosel, Regularizing and self-avoidance effects of integral Menger curvature, Ann. Sc. Norm. Super. Pisa Cl. Sci. 9 (2010) 145 MR2668877
22 J M Sullivan, Curves of finite total curvature, from: "Discrete differential geometry" (editors A I Bobenko, P Schröder, J M Sullivan, G M Ziegler), Oberwolfach Semin. 38, Birkhäuser, Basel (2008) 137 MR2405664
23 H J Sussmann, Shortest $3$–dimensional paths with a prescribed curvature bound, from: "Proc. of the 34th IEEE Conf. on Decision and Control", IEEE, New York (1995) 3306