论文标题
离散群体的dirichlet特征值的通用不平等
Universal inequalities for Dirichlet eigenvalues on discrete groups
论文作者
论文摘要
我们证明了在某些离散组子集对具有差异的Laplacian特征值的普遍不平等。 Weyl，Polya，Yau和其他人对Riemannian歧管的普遍不平等研究进行了研究。在这里，我们专注于Cheng和Yang的版本。 具体而言，我们证明了有限生成的amenable组的cayley图以及d-regular树（自由组中的简单随机步行）的杨型通用不等式。
We prove universal inequalities for Laplacian eigenvalues with Dirichlet boundary conditions on subsets of certain discrete groups. The study of universal inequalities on Riemannian manifolds was initiated by Weyl, Polya, Yau, and others. Here we focus on a version by Cheng and Yang. Specifically, we prove Yang-type universal inequalities for Cayley graphs of finitely generated amenable groups, as well as for the d-regular tree (simple random walk on the free group).
