The Gradient Flow of O'Hara's Knot Energies

2016/01/12 by Blatt, Simon · 1 citation
#35S10 #53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.02840

Abstract

Jun O'Hara invented a family of knot energies E^j,p, j,p ∈ (0, ∞). We study the negative gradient flow of the sum of one of the energies E^α= E^α,1, α∈ (2,3), 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.

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• Convergence of gradient flows on knotted curves

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