Spectrum of the Kohn Laplacian on the Rossi sphere

TL;DR

This paper investigates the spectrum of the Kohn Laplacian on the Rossi sphere, demonstrating that zero lies in its essential spectrum, which provides a new proof of the sphere's non-embeddability.

Contribution

It establishes that zero is in the essential spectrum of the Kohn Laplacian on the Rossi sphere, offering a novel proof of its non-embeddability.

Findings

Zero is in the essential spectrum of the Kohn Laplacian.

Provides a new proof of the Rossi sphere's non-embeddability.

Abstract

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