2002/03/20 by John M Sullivan, Sullivan, John M
Mathematics · #49Q10 #53A04 (Secondary) #57M25 (Primary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:49Q10 #msc:53A04 #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0203205
6 pages, 2 figures, LaTeX
arxiv created 2002/03/20 · arxiv updated 2009/11/30
The ropelength of a knot is the quotient of its length by its thickness. We consider a family of energy functions for knots, depending on a power p, which approach ropelength as p increases. We describe a numerically computed trefoil knot which seems to be a local minimum for ropelength; there are nearby critical points for the p-energies, which are evidently local minima for large enough p.