Abstract:We discuss a semi-implicit numerical scheme that allows for minimizing the bending energy of curves within certain isotopy classes. To this end we consider a weighted sum of the bending energy and the tangent-point functional. Based on estimates for the second derivative of the latter and a uniform bi-Lipschitz radius, we prove a stability result implying energy decay during the evolution as well as maintenance of arclength parametrization. Finally we present some numerical experiments exploring the energy landscape, targeted to the question how to obtain global minimizers of the bending energy in knot classes, so-called elastic knots.

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中文翻译：

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一种简单的弹性结和自避免不可扩展曲线逼近方案的稳定性

摘要：我们讨论了一种半隐式数值方案，该方案允许在某些同位素类别内最小化曲线的弯曲能。为此，我们考虑了弯曲能量和切点功能的加权和。基于后者的二阶导数和均匀的双Lipschitz半径的估计，我们证明了隐含在演化过程中能量衰减以及维持弧长参数化的稳定性结果。最后，我们提出了一些探索能量格局的数值实验，针对的问题是如何获得结类（即所谓的弹性结）中的弯曲能量的全局最小值。

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