论文标题
对称螺旋对的Möbius能量梯度的复杂渐近分数
Complex asymptotics of the Möbius energy gradient of symmetric helix pairs
论文作者
论文摘要
Möbius能量是一个良好的结结能，具有良好的规律性和自我抑制性能。 Möbius能量梯度下的固定曲线具有显着的理论利益，因为它们可以指示其自身力量下曲线的平衡状态。在本文中，我们考虑了MöbiusEnergy下的固定对称螺旋对。通过复杂的渐近学方法，我们将Möbius梯度的限制行为表征为盘绕比倾向于无穷大：根据半径是小于还是大于$ \ frac {1} {2} $，梯度将在相对方向上差异。 最后，我们讨论了对更通用的Möbius-Plateau能量的影响，其中曲线或一对曲线的能量包括由它们界定的最小表面的面积。对称螺旋对它们之间的螺旋螺旋形成，并应用我们的结果表明，固定的螺旋螺旋体从下面从下面开始生长到半径$ \ frac {1} {2} $，因为盘绕趋向于无穷大。
The Möbius energy is a well-studied knot energy with nice regularity and self-repulsive properties. Stationary curves under the Möbius energy gradient are of significant theoretical interest as they they can indicate equilibrium states of a curve under its own forces. In this paper, we consider stationary symmetric helix pairs under the Möbius energy. Through methods of complex asymptotics, we characterize the limiting behavior of the Möbius gradient as the coiling ratio tends to infinity: the gradient will diverge in opposing directions depending on whether the radius is less than or greater than $\frac{1}{2}$. We conclude by discussing the implications to the more general Möbius-Plateau energy, where the energy of a curve, or pair of curves, includes the area of the minimal surface bounded by them. Symmetric helix pairs bound a helicoid between them, and applying our result shows that stationary helicoids grow to radius $\frac{1}{2}$ from below as the coiling tends to infinity.
