论文标题
配对兼容的电气的光谱流
Spectral flow for pair compatible equipartitions
论文作者
论文摘要
我们表明，Berkolaiko-Cox-Marzuola提出的最近的光谱流方法可以将与本征功能相关的淋巴结分区的淋巴结缺乏扩展到更一般的分区。更确切地说，我们使用满足兼容条件的光谱等电气。节点分区和光谱最小分区是此类分区的示例。在此过程中，我们讨论了对Dirichlet到Neumann运营商的不同方法：通过Aharonov-Bohm操作员，通过双重覆盖论证以及通过域的缝制。
We show that a recent spectral flow approach proposed by Berkolaiko-Cox-Marzuola for analyzing the nodal deficiency of the nodal partition associated to an eigenfunction can be extended to more general partitions. To be more precise, we work with spectral equipartitions that satisfy a pair compatible condition. Nodal partitions and spectral minimal partitions are examples of such partitions. Along the way, we discuss different approaches to the Dirichlet-to-Neumann operators: via Aharonov-Bohm operators, via a double covering argument, and via a slitting of the domain.
