Local structure of ideal shapes of knots

Topology and its Applications

Volumn 154, Issue 17, 2007, Pages 3070-3089

  Durumeric, Oguz C ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Ideal knots; Normal injectivity radius; Thickness of knots

Indexed keywords

EID: 34548475294     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2007.07.004     Document Type: Article

References (21)

1. G. Buck, J. Simon, Energy and lengths of knots, in: Lectures at Knots 96, pp. 219-234
2. Cantarella J., Kusner R.B., and Sullivan J.M. On the minimum ropelength of knots and links. Invent. Math. 150 2 (2002) 257-286
3. Cheeger J., and Ebin D.G. Comparison Theorems in Riemannian Geometry vol. 9 (1975), North-Holland, Amsterdam
4. Diao Y. The lower bounds of the lengths of thick knots. J. Knot Theory Ramifications 12 1 (2003) 1-16
5. Dubins L.E. On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents. Amer. J. Math. 79 (1957) 497-516
6. 1, 1 Riemannian submanifolds. preprint. arXiv:math/0204050 [math.DG]
7. Durumeric O.C. Local structure of the ideal shapes of knots, II, Constant curvature case. preprint. arXiv:0706.1037v1 [math.GT]
8. Federer H. Geometric Measure Theory (1969), Springer
9. Freedman M., He Z.-X., and Wang Z. Mobius energy of knots and unknots. Ann. of Math. 139 (1994) 1-50
10. Gonzales O., and de La Llave R. Existence of ideal knots. J. Knot Theory Ramifications 12 (2003) 123-133
11. Gonzales O., and Maddocks H. Global curvature, thickness and the ideal shapes of knots. Proc. Nat. Acad. Sci. 96 (1999) 4769-4773
12. Gonzales O., Maddocks H., Schuricht F., and von der Mosel H. Global curvature and self-contact of nonlinearly elastic curves and rods. Calc. Var. Partial Differential Equations 14 (2002) 29-68
13. Katrich V., Bendar J., Michoud D., Scharein R.G., Dubochet J., and Stasiak A. Geometry and physics of knots. Nature 384 (1996) 142-145
14. A. Litherland, Unbearable thickness of knots, preprint
15. Litherland A., Simon J., Durumeric O., and Rawdon E. Thickness of knots. Topology Appl. 91 (1999) 233-244
16. Markov A.A. Some examples of the solution of a special kind of problem in greatest and least quantities. Soobbshch. Karkovsk. Mat. Obshch. 1 (1887) 250-276 (in Russian)
17. Nabutovsky A. Non-recursive functions, knots "with thick ropes" and self-clenching "thick" hyperspheres. Comm. Pure Appl. Math. 48 (1995) 381-428
18. Rawdon E., and Simon J. Mobius energy of thick knots. Topology Appl. 125 (2002) 97-109
19. Reeds J.A., and Shepp L.A. Optimal paths for a car that goes both forwards and backwards. Pacific J. Math. 145 (1990) 367-393
20. In: Stasiak A., Katrich V., and Kauffman L.H. (Eds). Ideal Knots (1998), World Scientific Publishing, Singapore
21. Sussmann H.J. Shortest 3-dimensional paths with a prescribed curvature bound. Proceedings of the 34th Conference on Decision and Control. New Orleans, LA, December 1995 (1995), IEEE Publications, New York 3306-3312