Eigenfunctions with Infinitely Many Isolated Critical Points
Eigenfunctions with Infinitely Many Isolated Critical Points
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DOI：
10.1093/imrn/rnz181
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发表时间：
2018-11
影响因子：
1
通讯作者：
Lev Buhovsky;A. Logunov;M. Sodin
中科院分区：
文献类型：
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作者：
Lev Buhovsky;A. Logunov;M. Sodin
我们在二维环面上构造黎曼度规，使得对于拉普拉斯-贝尔特拉米算子的无穷多个本征值，对应的本征函数具有无穷多个孤立临界点。我们的结构的一个小修改意味着这些特征函数中的每一个都有一个具有无限多个连接分量的水平集（即，两个特征函数的线性组合可能有无限多个节点域）。
We construct a Riemannian metric on the 2D torus, such that for infinitely many eigenvalues of the Laplace–Beltrami operator, a corresponding eigenfunction has infinitely many isolated critical points. A minor modification of our construction implies that each of these eigenfunctions has a level set with infinitely many connected components (i.e., a linear combination of two eigenfunctions may have infinitely many nodal domains).