Polygonal approximation and energy of smooth knots

Details Polygonal approximation and energy of smooth knots Polygonal approximation and energy of smooth knots

2003-05-29

arxiv.org/abs/math/0305414v1

Mathematics

Geometric Topology

29 pages, 5 figures

Scientific paper

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.

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