Polygonal approximation and energy of smooth knots

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dc.creatorRawdon, Eric J.
dc.creatorSimon, Jonathan K.
dc.date2003-05-29
dc.date.accessioned2026-07-07T04:58:22Z
dc.date.available2026-07-07T04:58:22Z
dc.descriptionWe 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.
dc.description29 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/math/0305414
dc.identifierhttp://arxiv.org/abs/math/0305414
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67608
dc.subjectGeometric Topology
dc.subject57M25
dc.titlePolygonal approximation and energy of smooth knots
dc.typetext

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