2003/05/29 by Eric J. Rawdon, Jonathan Simon, Rawdon, Eric J. +2
Engineering · Mathematics · #57M25 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0305414
29 pages, 5 figures
arxiv created 2003/05/29 · openalex publication_date 2003/05/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a fundamental connection between smooth and polygonal knot energies, showing that the Minimum Distance Energy for polygons inscribed in a smooth knot converges to the Moebius Energy of the smooth knot as the polygons converge to the smooth knot. However, the polygons must converge in a ``nice'' way, and the energies must be correctly regularized. We determine an explicit error bound between the energies in terms of the number of the edges of the polygon and the Ropelength of the smooth curve.