Circles Minimize most Knot Energies

Details Circles Minimize most Knot Energies Circles Minimize most Knot Energies

2001-05-16

arxiv.org/abs/math/0105138v1

Mathematics

Geometric Topology

15 pages with 3 figures. See also http://www.math.sc.edu/~howard/

Scientific paper

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.

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