Title

Polygonal approximation and energy of smooth knots

Department/School

Mathematics

Date

4-1-2006

Document Type

Article

Keywords

Knot energy, Möbius energy, Minimum Distance Energy, polygonal approximation

Abstract

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 Möbius Energy of the smooth knot as the polygons converge to the smooth knot. For this to work, the polygons must converge in a "nice" way, and the energies must be correctly regularized. We determine an explicit error bound for the convergence.

Volume

15

Issue

4

Published in

Journal of Knot Theory and Its Ramifications

Citation/Other Information

Rawdon, E.J. & Simon, J.K. (2006). Polygonal approximation and energy of smooth knots. Journal of Knot Theory and Its Ramifications, 15(4), 429–451.

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