Refinements to the Kuznetsov Formula for Laplace-Beltrami Operators

Merrick Chang

Refinements to the Kuznetsov Formula for Laplace-Beltrami Operators

Analysis of PDEs 2026-07-15 v1

Authors: Merrick Chang

Abstract

Wyman and Xi (2023) proved a Kuznetsov-type theorem for the submanifold counting function associated with Laplace--Beltrami eigenvalues. We refine the results of Wyman and Xi, improving their asymptotic: we remove a constant in the codimension-one case, and we prove a new asymptotic in the case that the set of looping times has measure zero.

Keywords

Kuznetsov formula Laplace-Beltrami operator submanifold counting function asymptotic eigenvalue

Cite

@article{arxiv.2607.14261,
  title  = {Refinements to the Kuznetsov Formula for Laplace-Beltrami Operators},
  author = {Merrick Chang},
  journal= {arXiv preprint arXiv:2607.14261},
  year   = {2026}
}

Comments

12 pages, 1 figure