Mathematics – Geometric Topology
Scientific paper
2004-11-03
Rus. J. of Math. Phys. v.9(2002),n3, 275-287 and The proc. of the conf. "Fund. Math. Today", MCCME(2003) 214-223
Mathematics
Geometric Topology
17 pages, 6 Postscript figures
Scientific paper
Let $E_f$ be the energy of some knot $\tau$ for any $f$ from certain class of functions. The problem is to find knots with extremal values of energy. We discuss the notion of the locally perturbed knot. The knot circle minimizes some energies $E_f$ and maximizes some others. So, is there any energy such that the circle neither maximizes nor minimizes this energy? Recently it was shown (A.Abrams, J.Cantarella, J.H.G.Fu, M.Ghomu, and R.Howard) that the answer is positive. We prove that nevertheless the circle is a locally extremal knot, i.e. the circle satisfies certain variational equations. We also find these equations. Finally we represent Mm-energy for a knot. The definition of this energy differs with one regarded above. Nevertheless besides its own properties Mm-energy has some similar with M\"obius energy properties.
No associations
LandOfFree
Energy of a knot: variational principles; Mm-energy does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Energy of a knot: variational principles; Mm-energy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Energy of a knot: variational principles; Mm-energy will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-48236