Title

Error analysis of the Minimum Distance Energy of a polygonal knot and the Moebius Energy of an approximating curve

Department/School

Mathematics

Date

8-1-2010

Document Type

Article

Keywords

rope length, knots, tight knots, ideal knots

Abstract

Energy minimizing smooth knot configurations have long been approximated by finding knotted polygons that minimize discretized versions of the given energy. However, for most knot energy functionals, the question remains open on whether the minimum polygonal energies are "close" to the minimum smooth energies. In this paper, we determine an explicit bound between the Minimum-Distance Energy of a polygon and the Möbius Energy of a piecewise-C2 knot inscribed in the polygon. This bound is written in terms of the ropelength and the number of edges and can be used to determine an upper bound for the minimum Möbius Energy for different knot types.

Published in

Journal of Knot Theory Ramifications

Citation/Other Information

Rawdon, E. J. and Worthington, J. (2010). Error analysis of the minimum distance energy of a polygonal knot and the Möbius energy of an approximating curve. Journal of Knot Theory and Its Ramifications, 19 (8) 975–1000. https://doi.org/10.1142/S0218216510008303.

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