• DOI:10.1186/s13662-022-03750-4
• Corpus ID: 247794082

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

@article{Lagemann2022TangentpointEA,
  title={Tangent-point energies and ropelength as Gamma-limits of discrete tangent-point energies on biarc curves},
  author={Anna Lagemann and Heiko von der Mosel},
  journal={Advances in Continuous and Discrete Models},
  year={2022},
  volume={2023}
}

• Anna Lagemann, H. von der Mosel
• Published 30 March 2022
• Mathematics
• Advances in Continuous and Discrete Models

Using interpolation with biarc curves we prove Γ-convergence of discretized tangent-point energies to the continuous tangent-point energies in the C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C^{1}$\end{document}-topology, as well as to the ropelength functional. As a consequence, discrete almost minimizing biarc curves converge to minimizers of the continuous tangent-point energies, and to ropelength minimizers, respectively. In addition, taking point-tangent data from a given C1,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$C^{1,1}$\end{document}-curve γ, we establish convergence of the discrete energies evaluated on biarc curves interpolating these data, to the continuous tangent-point energy of γ, together with an explicit convergence rate.