Polygonal approximation and energy of smooth knots
Knot energy, Möbius energy, Minimum Distance Energy, polygonal approximation
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.
Journal of Knot Theory and Its Ramifications