论文标题
分解的Möbius能量连续性的上和下边界和模量
Upper and lower bounds and modulus of continuity of decomposed Möbius energies
论文作者
论文摘要
MöbiusEnergy是结的能量之一，以其Möbius不变特性命名。众所周知，它具有几种不同的表达方式。就保形角余弦而言，被称为余弦公式。另一个是分解成Möbius不变部分的分解，称为分解的MöbiusEnergies。因此，余弦公式是分解能量的总和。这提出了一个问题。每个分解的能量可以通过余弦公式估计吗？在这里，我们给出一个肯定的答案：可以根据余弦公式评估分解部分的上限和下限。此外，我们还提供了两条曲线之间分解能量在Möbius不变数量方面的差异。
The Möbius energy is one of the knot energies, and is named after its Möbius invariant property. It is known to have several different expressions. One is in terms of the cosine of conformal angle, and is called the cosine formula. Another is the decomposition into Möbius invariant parts, called the decomposed Möbius energies. Hence the cosine formula is the sum of the decomposed energies. This raises a question. Can each of the decomposed energies be estimated by the cosine formula~? Here we give an affirmative answer: the upper and lower bounds, and modulus of continuity of decomposed parts can be evaluated in terms of the cosine formula. In addition, we provide estimates of the difference in decomposed energies between the two curves in terms of Möbius invariant quantities.
