An Analog of the Weyl Law for the Kohn Laplacian on Spheres

TL;DR

This paper derives an explicit formula for the leading term in the asymptotic eigenvalue count of the Kohn Laplacian on spheres, extending the classical Weyl law to a CR geometric setting.

Contribution

It provides the first explicit asymptotic formula for the eigenvalue distribution of the Kohn Laplacian on spheres, analogous to Weyl's law in Riemannian geometry.

Findings

Explicit leading coefficient formula for eigenvalue asymptotics

Extension of Weyl law to CR geometry on spheres

Enhanced understanding of spectral geometry of the Kohn Laplacian

Abstract

We present an explicit formula for the leading coefficient in the asymptotic expansion of the eigenvalue counting function of the Kohn Laplacian on the unit sphere $\mathbb{S}^{2n-1}$.