Sub-Laplacian eigenvalue bounds on CR manifolds

TL;DR

This paper establishes universal upper bounds for sub-Laplacian eigenvalues on CR manifolds, aligning with known asymptotic laws and extending classical eigenvalue bounds to the CR geometric setting.

Contribution

It introduces eigenvalue bounds for CR manifolds that are independent of pseudo-Hermitian structures, generalizing classical Laplacian bounds to CR geometry.

Findings

Upper bounds are independent of pseudo-Hermitian structure.

Bounds are compatible with Menikoff-Sjoestrand asymptotics.

CR version of Korevaar's eigenvalue bounds.

Abstract

We prove upper bounds for sub-Laplacian eigenvalues independent of a pseudo-Hermitian structure on a CR manifold. These bounds are compatible with the Menikoff-Sjoestrand asymptotic law, and can be viewed as a CR version of Korevaar's bounds for Laplace eigenvalues of conformal metrics.