308 research outputs found
The Gradient Flow of O'Hara's Knot Energies
Jun O'Hara invented a family of knot energies , . We study the negative gradient flow of the sum of one of the energies
, , and a positive multiple of the
length.
Showing that the gradients of these knot energies can be written as the
normal part of a quasilinear operator, we derive short time existence results
for these flows. We then prove long time existence and convergence to critical
points.Comment: 45 page
Stationary Points of O'Hara's Knot Energies
In this article we study the regularity of stationary points of the knot
energies introduced by O'Hara in the range . In a
first step we prove that is on the set of all regular embedded
closed curves belonging to and calculate its derivative.
After that we use the structure of the Euler-Lagrange equation to study the
regularity of stationary points of plus a positive multiple of the
length. We show that stationary points of finite energy are of class
- so especially all local minimizers of among curves with fixed
length are smooth.Comment: Corrected typo
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