We give a geometric interpretation for
the Euler-Lagrange equation for the Möbius
cross energy of (nontrivially linked) 2-component links in
the euclidean 3-space.
The minimizer of this energy is conjectured
to be a Hopf link of 2 round circles. We prove some elementary
properties of the minimizers using the Euler-Lagrange equations.
In particular, we give a rigorous proof of the fact that the
minimizer is topologically a Hopf link.
@article{1062621218,
author = {He, Zheng-Xu},
title = {On the minimizers of the M\"obius cross energy of links},
journal = {Experiment. Math.},
volume = {11},
number = {3},
year = {2002},
pages = { 244-248},
language = {en},
url = {http://dml.mathdoc.fr/item/1062621218}
}
He, Zheng-Xu. On the minimizers of the Möbius cross energy of links. Experiment. Math., Tome 11 (2002) no. 3, pp. 244-248. http://gdmltest.u-ga.fr/item/1062621218/