A lower bound for the energy of magnetic fields supported in linked tori;Une borne inférieure pour l'énergie de champs magnétiques à support dans des tores liés

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 331, Issue 3, 2000, Pages 201-206

  Laurence, Peter ^a,b   Stredulinsky, Edward ^c  

^a NEW YORK UNIVERSITY   (United States)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c 53581   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034238552     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(00)01598-6     Document Type: Article

References (17)

1. [1] Arnol'd V.I., The asymptotic Hopf invariant and it's applications (in Russian), Proc. Summer School in Differ. Eq., Eravan, 1974. [English translation: Sel. Math. Sov. 327 (5) (1986).]
2. [2] Arnol'd V.I., Topological Fluid Dynamics, Springer, (to appear)
3. [3] Berger M.-A., Third order link integrals, J. Math. Gen. 23 (1990) 2787-2793.
4. [4] Cantarella J., de Turk D., Gluck H., Teytel M., Isoperimetric problems for helicity of vector fields and the Biot-Savart and curl operators, Preprint, 1999.
5. [5] Friedman, H., Divergence free fields: energy and asymptotic crossing number, Ann. Math. 134 (1) (1991) 219-254.
6. [6] Fuglede B., Extremal length and functional completion, Acta. Math. 98 (1957) 171-219.
7. [7] Kotiuga R., On making cuts for magnetic scalar potentials in multiply connected regions, J. Appl. Phys. 61 (8) (1987).
8. [8] Laurence P., Stredulinsky E., Asymptotic Massey products, induced currents and Borromean torus links, J. Math. Phys. 41 (5) (2000).
9. [9] Laurence P., Stredulinsky E., Third order helicity: induced currents and lower bounds on the magnetic energy, Universitè di Roma I, Report 8/98, 1998.
10. [10] Laurence P., Stredulinsky E., (in preparation).
11. [11] Laurence P., Avellaneda M., Moffatt A., Arnol'd formula for the mutual helicity of linked flux tubes, Geo. Astro. Fluid Dynam. 69 (1993) 243-256.
12. [12] Lieb E.H., Sharp constants in the Hardy Littlewood Sobolev and related inequalities, Ann. Math. 118 (1983) 349-374.
13. [13] Massey W.S., Some higher order cohomology operations, Symp. Int. de Top. Alg., Mexico City (1958).
14. [14] Massey W.S., Higher order linking numbers, Conf. on Algebraic Topology, University of Chicago, Chicago Circle, Chicago, Ilinois, 1968, pp. 174-205.
15. [15] Meeks, William H., Patrusky J., Representing codimension one homology classes by embedded submanifolds, Pacific J. Math. 68 (1) (1977) 175-176.
16. [16] Moffatt H.K., The degree of knottedness of tangled field lines, J. Fluid Mech. 35 (1969) 117.
17. [17] Monastyrsky M.I., Retakh V, Topology of linked defects in condensed matter, Commun. Math. Phys. 103 445-4559.