No. 2022.04
Tangent-point energies and ropelength as Gamma-limit of discrete tangent-point energies on biarc curves
A. Lagemann and H. von der Mosel
Subject: Ropelength, tangent-point energy, discretization, biarcs, Gamma convergence
Abstract
Using interpolation with biarc curves we prove $\Gamma$-convergence of discretized tangent-point energies to the continuous tangent-point energies in the $C^1$-topology, as well as to the ropelength functional. As a consequence discrete almost minimizing biarc curves converge to ropelength minimizers, and to minimizers of the continuous tangent-point energies. In addition, taking point-tangent data from a given $C^{1,1}$-curve $\gamma$, we establish convergence of the discrete energies evaluated on biarc curves interpolating these data, to the continuous tangent-point energy of $\gamma$, together with an explicit convergence rate.
Reference
Adv. Contin. Discrete Models 2023, Paper No. 4, 33 pp.