Elastic knots in euclidean 3-space

Heiko von der Mosel

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 2, page 137-166
  • ISSN: 0294-1449

How to cite

top

von der Mosel, Heiko. "Elastic knots in euclidean 3-space." Annales de l'I.H.P. Analyse non linéaire 16.2 (1999): 137-166. <http://eudml.org/doc/78461>.

@article{vonderMosel1999,
author = {von der Mosel, Heiko},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {curvature functionals; existence in isotopy classes; closed knotted curves},
language = {eng},
number = {2},
pages = {137-166},
publisher = {Gauthier-Villars},
title = {Elastic knots in euclidean 3-space},
url = {http://eudml.org/doc/78461},
volume = {16},
year = {1999},
}

TY - JOUR
AU - von der Mosel, Heiko
TI - Elastic knots in euclidean 3-space
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 2
SP - 137
EP - 166
LA - eng
KW - curvature functionals; existence in isotopy classes; closed knotted curves
UR - http://eudml.org/doc/78461
ER -

References

top
  1. [1] R. Bryant and P. Griffiths, Reduction of Order for the Constrained Variational Problem and ∫ k2/2 ds, Amer. J. Math., 108, 1986, pp. 525-570 . Zbl0604.58022MR844630
  2. [2] U. Dierkes, S. Hildebrandt, A. Küster and O. Wohlrab, Minimal Surfaces I (Boundary Value Problems), II (Boundary Regularity), Grundlehren der math. Wissenschaften, vols. 295-296, Springer, BerlinHeidelbergNew York, 1992. Zbl0777.53012MR1215267
  3. [3] L. Euler, Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattisimo sensu accepti, Bousquet, Lausannae et Genevae, 1744, E 65A. O.O. Ser. I, vol. 24. Zbl0788.01072
  4. [4] M.H. Freedman, ZHENG-XU He and Zhenghan Wang, On the Möbius Energy of Knots and Unknots, Annals of Math., 139 no. 1, 1994, pp. 1-50. Zbl0817.57011MR1259363
  5. [5] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Annals of Math. Studies105, Princeton Univ. Press, 1983. Zbl0516.49003MR717034
  6. [6] S. Hildebrandt and H.C. Wente, Variational Problems with Obstacles and a Volume Constraint, Math. Z.135, 1973, pp. 55-68. Zbl0284.49017MR365314
  7. [7] R. Irrgang, Ein singuläres bewegungsinvariantes Variationsproblem, Math. Z., 37, 1933, pp. 381-401. Zbl0007.21301MR1545401
  8. [8] R. Kusner and J. Sullivan, Möbius Energies for Knots and Links, Surfaces and Submanifolds, Geometric Topology, Proc. Georgia International Topology Conference, 1993, (ed. W.H. Kazez), AMS/IP Studies in Advanced Math., vol. 2, 1996, pp. 570-604. Zbl0888.57012MR1470748
  9. [9] J. Langer and D.A. Singer, Knotted Elastic Curves in R3, J. London Math. Soc., (2), 30, 1984, pp. 512-520. Zbl0595.53001MR810960
  10. [10] J. Langer and D.A. Singer, Curves in the Hyperbolic Plane and Mean Curvature of Tori in 3-Space, Bull. London Math. Soc., 16, 1984, pp. 531-534. Zbl0554.53014MR751827
  11. [11] J. Langer and D.A. Singer, The Total Squared Curvature of Closed Curves, J. Differential Geometry , 20, 1984, pp. 1-22. Zbl0554.53013MR772124
  12. [12] J. Langer and D.A. Singer, Curve Straightening and a Minimax Argument for Closed Elastic Curves, Topology, 24, no. 1, 1985, pp. 75-88. Zbl0561.53004MR790677
  13. [13] J. O'Hara, Energy of a Knot, Topology, 30, 1991, pp. 241-247. Zbl0733.57005MR1098918
  14. [14] A. Polden, Closed Curves of Least Total Curvature, Preprint, SFB 382 Univ. Tübingen, Report Nr.13 (1995). 
  15. [15] J. Radon, Über das Minimum des Integrals ∫s2 s1 F(x, γ, υ, κ)ds, Sitzungsber. Kaiserliche Akad. Wiss., Wien. Math.-nat. Kl., 69, 1910, pp. 1257-1326. JFM41.0438.01
  16. [16] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966. Zbl0149.09501MR209834
  17. [17] E.W. Stredulinsky, Higher Integrability from Reverse Hölder Inequalities, Indiana Univ. Math. J., 29, no. 3, 1980, pp. 407-413. Zbl0442.35064MR570689
  18. [18] H. Von Der Mosel, Geometrische Variationsprobleme höherer Ordnung, Bonner Math. Schriften, 293, 1996. Zbl0888.49031MR1614881

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.