Spectral estimates for the Heisenberg Laplacian on cylinders

TL;DR

This paper investigates the spectral properties of the Heisenberg Laplacian on cylindrical domains, deriving precise eigenvalue estimates with sharp leading terms and lower order corrections.

Contribution

It provides the first sharp spectral inequality for the Heisenberg Laplacian on cylinders, including lower order terms.

Findings

Derived a sharp inequality for Riesz means of eigenvalues

Included lower order correction terms in the spectral estimate

Enhanced understanding of spectral behavior on cylindrical domains

Abstract

We study Riesz means of eigenvalues of the Heisenberg Laplacian with Dirichlet boundary conditions on a cylinder in dimension three. We obtain an inequality with a sharp leading term and an additional lower order term.