The first positive eigenvalue of the sub-Laplacian on CR spheres

Abstract

We prove that the first positive eigenvalue, normalized by the volume, of the sub-Laplacian associated with a strictly pseudo-convex pseudo-Hermitian structure \(\theta \) on the CR sphere \(\mathbb {S}^{2n+1}\subset \mathbb {C}^{n+1}\), achieves its maximum when \(\theta \) is the standard contact form.