排斥-吸引势聚集平衡的径向对称性与分形行为
From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials
摘要：
对于具有排斥-吸引势的相互作用能，我们给出了在无限Wasserstein距离下保证局部极小值径向对称的一般条件。作为结果，我们得到了局部极小在这个拓扑的一类相互作用势的唯一性。我们引入了一个新的概念的相互作用势的的分形，使我们能够显示某些分形的局部极小的行为。我们提供了一个家庭的相互作用潜力，使相关的本地极小的支持没有孤立点和任何superlevel集没有内点。
英文摘要：
For the interaction energy with repulsive-attractive potentials, we give generic conditions which guarantee the radial symmetry of the local minimizers in the infinite Wasserstein distance. As a consequence, we obtain the uniqueness of local minimizers in this topology for a class of interaction potentials. We introduce a novel notion of concavity of the interaction potential allowing us to show certain fractal-like behavior of the local minimizers. We provide a family of interaction potentials such that the support of the associated local minimizers has no isolated points and any superlevel set has no interior points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
