Thickness of knots

Topology and its Applications

Volumn 91, Issue 3, 1999, Pages 233-244

  Litherland, R A ^a   Simon, J ^b   Durumeric, O ^b   Rawdon, E ^b  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

Curvature; Distortion; Edge number; Knots; Self distance; Thickness

Indexed keywords

EID: 0000633669     PISSN: 0016660X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0166-8641(97)00210-1     Document Type: Article

References (17)

1. G. Buck, On the energy and length of a knot, Special Session on Physical Knot Theory (Amer. Math. Soc., Iowa City, March 1996).
2. M. Perdigão do Carmo, Riemannian Geometry (Birkhäuser, Boston, 1992); originally published in Portuguese as Geometria Riemanniana (Instituto de Matematica Pura e Aplicada, 1979; 2nd ed., 1988).
3. M. Perdigão do Carmo, Riemannian Geometry (Birkhäuser, Boston, 1992); originally published in Portuguese as Geometria Riemanniana (Instituto de Matematica Pura e Aplicada, 1979; 2nd ed., 1988).
4. Y. Diao, K. Ernst and E.J.J. Van Rensburg, Energies of knots, Preprint (3/95); Knot energies by ropes, Preprint (4/96).
5. Y. Diao, K. Ernst and E.J.J. Van Rensburg, Energies of knots, Preprint (3/95); Knot energies by ropes, Preprint (4/96).
6. M. Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1-147 (see p. 113).
7. N. Kuiper, Pers. corresp. with J. O'Hara, see O'Hara, loc. cit.
8. R. Litherland, Thickness of knots, Workshop on 3-Manifolds (University of Tennessee, 1992).
9. J. Milnor, On the total curvature of knots, Ann. of Math. 52 (1950) 248-257.
10. A. Nabutovsky, Nonrecursive functions, knots "with thick ropes", and self-clenching "thick" hyperspheres, Comm. Pure Appl. Math. 48 (4) (1995) 381-428.
11. J. O'Hara, Family of energy functionals of knots, Topology Appl. 48 (1992) 147-161.
12. R. Randell, An elementary invariant of knots, J. Knot Theory Ramifications 3 (1994) 279-286.
13. J. Simon, Thickness of knots, Special Session on Knotting Phenomena in the Natural Sciences (Amer. Math. Soc., Santa Barbara, November 1991); Lecture Notes on Physical Knot Theory (notes by H. Naka), 1993, from summer 1991 course, Kwansei Gakuin University.
14. J. Simon, Thickness of knots, Special Session on Knotting Phenomena in the Natural Sciences (Amer. Math. Soc., Santa Barbara, November 1991); Lecture Notes on Physical Knot Theory (notes by H. Naka), 1993, from summer 1991 course, Kwansei Gakuin University.
15. M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. I (Publish or Perish, Inc., Boston, 1970).
16. A. Stasiak, Ideal forms of knots, Special Session on Physical Knot Theory (Amer. Math. Soc., Iowa City, March 1996).
17. J.A. Thorpe, Elementary Topics in Differential Geometry, Undergrad. Texts Math. (Springer, New York, 1979).