Spectral Analysis of the Kohn Laplacian on Lens Spaces

TL;DR

This paper establishes a Weyl law analogue for the Kohn Laplacian on lens spaces and characterizes when two such spaces are isospectral, linking spectral data to geometric CR isometry.

Contribution

It provides a spectral characterization of lens spaces via the Kohn Laplacian, connecting isospectrality with CR isometry in three dimensions.

Findings

Derived an analogue of Weyl's law for the Kohn Laplacian on lens spaces.

Proved that isospectral lens spaces with prime order fundamental groups are CR isometric.

Established a spectral-geometry correspondence for 3-dimensional lens spaces.

Abstract

We obtain an analog of Weyl's law for the Kohn Laplacian on lens spaces. We also show that two 3-dimensional lens spaces with fundamental groups of equal prime order are isospectral with respect to the Kohn Laplacian if and only if they are CR isometric.