Pure and Applied Mathematics Quarterly

Volume 18 (2022)

Number 6

Special issue in honor of Fan Chung

Guest editors: Paul Horn, Yong Lin, and Linyuan Lu

Eigenvalue sum estimates for lattice subgraphs

Pages: 2339 – 2353

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n6.a1


Frank Bauer

Gabor Lippner (Northeastern University, Boston, Massachusetts, U.S.A.)


We prove sharp upper and lower bounds, up to an error term, on the sum of the first $k$ Dirichlet eigenvalues of induced subgraphs of the $d$-dimensional lattice.

Received 16 June 2021

Accepted 13 September 2021

Published 29 March 2023