Erratum to Regularized Riesz energies of submanifolds
Erratum to Regularized Riesz energies of submanifolds
复制标题
子流形正则化 Riesz 能量的勘误
DOI：
10.1002/mana.202000024
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Jun O'Hara and Gil Solanes
中科院分区：
文献类型：
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作者：
Jun O'Hara and Gil Solanes
给定欧几里得空间中的闭合子流形或紧致正则域，我们将里斯能量定义为点对之间距离的某些幂的二重积分。当该积分发散时，我们比较两种不同的正则化技术（哈达玛有限部分和解析延拓），并表明它们给出的结果本质上相同。我们证明其中一些能量在莫比乌斯变换下是不变的，从而概括了更高维度的莫比乌斯能量结。
Given a closed submanifold, or a compact regular domain, in Euclidean space, we consider the Riesz energy defined as the double integral of some power of the distance between pairs of points. When this integral diverges, we compare two different regularization techniques (Hadamard's finite part and analytic continuation), and show that they give essentially the same result. We prove that some of these energies are invariant under Möbius transformations, thus giving a generalization to higher dimensions of the Möbius energy of knots.