The invariance of the decomposed Mobius energies under the inversions with center on curves
The invariance of the decomposed Mobius energies under the inversions with center on curves
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曲线中心反演下分解莫比乌斯能的不变性
DOI：
10.1142/s0218216516500097
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发表时间：
2016
影响因子：
0.5
通讯作者：
Takeyuki Nagasawa
中科院分区：
文献类型：
--
作者：
Aya Ishizeki;Takeyuki Nagasawa
众所周知，奥哈拉的结能量之一被称为莫比乌斯能量，因为它在莫比乌斯变换下不变性。我们在以前的论文中表明，莫比乌斯能量可以分解为三个部分，保持不变，但我们留下了开放的问题，关于反演的不变性方面的领域为中心的一个结。在这里，我们回答这个问题的假设下，结有额外的规则性。该结果不仅适用于节点，而且适用于中的闭合曲线。
It is well known that one of O’Hara’s knot energies is called the Möbius energy because of its invariance under Möbius transformations. We showed in a previous paper that the Möbius energy can be decomposed into three parts that retain invariance but we left open the question of invariance regarding inversions with respect to spheres centered on a knot. Here, we answer this question under the assumption that the knots have extra regularity. The result holds not only for knots but also for closed curves in.