Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip
Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip
复制标题
莫比乌斯带上狄利克雷本征函数的 Courant-sharp 性质
DOI：
10.4171/pm/2059
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发表时间：
2020
影响因子：
0.8
通讯作者：
R. Kiwan
中科院分区：
文献类型：
--
作者：
Pierre B'erard;B. Helffer;R. Kiwan
确定哪些特征值存在与相关特征值的标签具有相同数目的节点域的特征函数（Courant-sharp性质）的问题是由最小谱划分的分析激发的。在以前的作品中，已经分析了许多例子对应的正方形，矩形，磁盘，三角形，圆环，。.. .一个自然的玩具模型，为进一步的研究是莫比乌斯带，一个不可定向的表面与欧拉特征为0，特别是“平方”莫比乌斯带的特征值有较高的多重性。在这种情况下，我们证明了唯一的Courant-sharp Dirichlet特征值是第一和第二，我们表现出独特的节点模式。
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,. .. . A natural toy model for further investigations is the Mobius strip, a non-orientable surface with Euler characteristic 0, and particularly the "square" Mobius 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.