We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ · ‖ W1,∞(S1,ℝd). This result directly implies the convergence of almost minimizers of the discrete energies in a fixed knot class to minimizers of the smooth energy.Moreover,we show that the unique absolute minimizer of inverse discrete thickness is the regular n-gon.
@article{bwmeta1.element.doi-10_2478_mlbmb-2014-0005,
author = {Sebastian Scholtes},
title = {Discrete thickness},
journal = {Molecular Based Mathematical Biology},
volume = {2},
year = {2014},
zbl = {1312.49054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_mlbmb-2014-0005}
}
Sebastian Scholtes. Discrete thickness. Molecular Based Mathematical Biology, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_mlbmb-2014-0005/
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