Spectrum of the Kohn Laplacian on the Rossi sphere

Abstract

We study the spectrum of the Kohn Laplacian ${\square }_b^t$ on the Rossi example $\left({\mathbb{S}}^3,{\mathcal{ℒ}}_t\right)$. In particular we show that $0$ is in the essential spectrum of ${\square }_b^t$, which yields another proof of the global nonembeddability of the Rossi example.