双纽动物无法在拉普拉斯增长中存活
Lemniscates do not survive Laplacian growth
摘要：
由所谓的拉普拉斯增长模型化的平面中的大类移动边界过程，其描述例如，固化、电沉积、粘性指进、细菌生长等，已知是可积的，并具有大量的精确解。在这项工作中，边界被假定为在类双纽线与所有零内的有界组件的复平面。我们证明，从这个类的任何初始边界，不断发展的边界立即停止在类中，否则拉普拉斯增长立即摧毁双纽。
英文摘要：
The large class of moving boundary processes in the plane modeled by the so-called Laplacian growth, which describes, e.g., solidification, electrodeposition, viscous fingering, bacterial growth, etc., is known to be integrable and to exhibit a large number of exact solutions. In this work, the boundaries are assumed to be in the class of lemniscates with all zeros inside the bounded component of the complex plane. We prove that for any initial boundary taken from this class, the evolving boundary instantly stops being in the class, or else Laplacian growth destroys lemniscates instantly.
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