Universal inequalities for Dirichlet eigenvalues on discrete groups

Bobo Hua, Ariel Yadin

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Abstract

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).
Original languageEnglish GB
JournalarXiv
StatePublished - 1 Jul 2020

Keywords

  • Mathematics - Differential Geometry
  • Mathematics - Group Theory
  • Mathematics - Probability

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