The second hull of a knotted curve

American Journal of Mathematics

Volumn 125, Issue 6, 2003, Pages 1335-1348

  Cantarella, Jason ^a   Kuperberg, Greg ^b   Kusner, Robert B ^c   Sullivan, John M ^d  

^a UNIVERSITY OF GEORGIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF MASSACHUSETTS   (United States)

^d UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346957394     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.2003.0038     Document Type: Article

References (20)

1. [AB98] S. B. Alexander and R. L. Bishop, The Fáry-Milnor theorem in Hadamard manifolds, Proc. Amer. Math. Soc. 126 (1998), 3427-3436.
2. [CKS02] J. Cantarella, R. B. Kusner, and J. M. Sullivan, On the minimum ropelength of knots and links, Invent. Math. 150 (2002), 257-286, arXiv:math.GT/0103224.
3. [CC97] T. E. Cecil and S.-S. Chem (eds.), Tight and Taut Submanifolds, Cambridge University Press, Cambridge, 1997.
4. [CSY87] R. Cole, M. Sharir, and C.-K. Yap, On k-hulls and related problems, SIAM J. Comput. 16 (1987), 61-77.
5. [EWW02] T. Ekholm, B. White, and D. Wienholtz, Embeddedness of minimal surfaces with total boundary curvature at most 4π, Ann. of Math. 1551 (2002), 109-234.
6. [Fár49] I. Fáry, Sur la courbure totale d'une courbe gauche faisant un nœud, Bull. Soc. Math. France 77 (1949), 128-138.
7. [FHW94] M. H. Freedman, Z.-X. He, and Z. Wang, On the Möbius energy of knots and unknots, Ann. of Math. 139 (1994), 1-50.
8. [Gab87] D. Gabai, Foliations and the topology of 3-manifolds. III, J. Differential Geom. 26 (1987), 479-536.
9. [Gag80] M. E. Gage, A proof of Gehring's linked spheres conjecture, Duke Math. J. 47 (1980), 615-620.
10. [Gro83] M. Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983), 1-147.
11. [Kui87] N. H. Kuiper, A new knot invariant, Math. Ann. 278 (1987), 193-209.
12. [Kup94] G. Kuperberg, Quadrisecants of knots and links, J. Knot Theory Ramifications 31 (1994), 41-50, arXiv:math.GT/9712205.
13. [KS97] R. B. Kusner and J. M. Sullivan, Möbius energies for knots and links, surfaces and submanifolds, Proceedings of the Georgia Int'l Topology Conference, August 1993, Geometric Topology (Willam H. Kazez, ed.), Amer. Math. Soc./Internat. Press, 1997, pp. 570-604.
14. [Mil50] J. W. Milnor, On the total curvature of knots, Ann. of Math. 52 (1950), 248-257.
15. [MM82] H. R. Morton and D. M. Q. Mond, Closed curves with no quadrisecants, Topology 21 (1982), 235-243.
16. [Pan33] E. Pannwitz, Eine elementargeometrishe Eigenschaft von Verschlingungen und Knoten, Math. Ann. 108 (1933), 629-672.
17. [Rol76] D. Rolfsen, Knots and Links, Publish or Perish, Wilmington, 1976.
18. [Sch98] C. Schmilz, The theorem of Fáry and Milnor for Hadamard manifolds, Geom. Dedicata 71 (1998), 83-90.
19. [Tho97] A. Thompson, Thin position and bridge number for knots in the 3-sphere, Topology 36 (1997), 505-507.
20. [Whi96] B. White, Half of Enneper's surface minimizes area, Geometric Analysis and the Calculus of Variations (Jürgen Jost, ed.), Internat. Press, Cambridge, MA, 1996, pp. 361-367.