Circles Minimize most Knot Energies
Geometric Topology
2007-05-23 v1 Differential Geometry
Abstract
We define a new class of knot energies (known as renormalization energies) and prove that a broad class of these energies are uniquely minimized by the round circle. Most of O'Hara's knot energies belong to this class. This proves two conjectures of O'Hara and of Freedman, He, and Wang. We also find energies not minimized by a round circle. The proof is based on a theorem of G. Luko on average chord lengths of closed curves.
Keywords
Cite
@article{arxiv.math/0105138,
title = {Circles Minimize most Knot Energies},
author = {Aaron Abrams and Jason Cantarella and Joseph H. G. Fu and Mohammad Ghomi and Ralph Howard},
journal= {arXiv preprint arXiv:math/0105138},
year = {2007}
}
Comments
15 pages with 3 figures. See also http://www.math.sc.edu/~howard/