# Spectra of Kohn Laplacians on Spheres

## TL;DR

This paper analyzes the spectrum of the Kohn Laplacian on spheres in complex space, revisiting classical eigenvalue computations and exploring eigenvalue growth rates for both standard and perturbed cases.

## Contribution

It provides a detailed study of the eigenvalues of the Kohn Laplacian on spheres and extends the analysis to the Rossi sphere with perturbed operators.

## Key findings

- Revisited Folland's classical eigenvalue computation.
- Analyzed the growth rate of the eigenvalue counting function.
- Examined eigenvalue growth of the perturbed Kohn Laplacian on the Rossi sphere.

## Abstract

In this note, we study the spectrum of the Kohn Laplacian on the unit spheres in $\mathbb{C}^n$ and revisit Folland's classical eigenvalue computation. We also look at the growth rate of the eigenvalue counting function in this context. Finally, we consider the growth rate of the eigenvalues of the perturbed Kohn Laplacian on the Rossi sphere in $\mathbb{C}^2$.