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arXiv · 2203.16383

Tangent-point energies and ropelength as Gamma-limit of discrete tangent-point energies on biarc curves

Anna Lagemann·Heiko von der Mosel
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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.

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BibTeXRIS

Anna Lagemann, Heiko von der Mosel. 2022-03-30. Tangent-point energies and ropelength as Gamma-limit of discrete tangent-point energies on biarc curves. https://arxiv.org/abs/2203.16383

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