论文标题
courant-sharp属性，用于莫比乌斯脱衣舞的dirichlet eigenfunctions
Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip
论文作者
论文摘要
确定存在哪种特征值的特征功能的问题，该特征功能具有与相关特征值（Courant-Sharp属性）标签相同的汇总域（Courant-Sharp属性）的动机，这是通过最小光谱分区的分析来激励的。在以前的作品中，已经分析了许多示例，对应于平方，矩形，磁盘，三角形，托里，\ ldots。用于进一步研究的天然玩具模型是Möbius条，它是一种不可定向的表面，具有Euler特征$ 0 $，尤其是“正方形”Möbius带，其特征值具有较高的多重性。在这种情况下，我们证明了唯一的courant-sharp dirichlet特征值是第一个和第二个，我们表现出奇特的鼻模式。
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions. In previous works, many examples have been analyzed corresponding to squares, rectangles, disks, triangles, tori, \ldots . A natural toy model for further investigations is the Möbius strip, a non-orientable surface with Euler characteristic $0$, and particularly the "square" Möbius strip whose eigenvalues have higher multiplicities. In this case, we prove that the only Courant-sharp Dirichlet eigenvalues are the first and the second, and we exhibit peculiar nodal patterns.
