论文标题
小扰动下的拉普拉斯本征函数的结节集
Nodal sets of Laplace eigenfunctions under small perturbations
论文作者
论文摘要
我们研究了特定小扰动下紧凑型歧管上拉普拉斯特征函数的淋巴结集的稳定性。我们证明，如果上述扰动相对较小，更正式，以次波长尺度支撑，则淋巴结集相当稳定。我们不需要关于节点集拓扑的任何假设。作为间接应用程序，我们能够证明在域的受控扰动下，有关第二个节点线的某些“ Payne属性”保持稳定。
We study the stability properties of nodal sets of Laplace eigenfunctions on compact manifolds under specific small perturbations. We prove that nodal sets are fairly stable if said perturbations are relatively small, more formally, supported at a sub-wavelength scale. We do not need any assumption on the topology of the nodal sets. As an indirect application, we are able to show that a certain "Payne property" concerning the second nodal line remains stable under controlled perturbations of the domain.
