A Cheeger-type Inequality for the Sub-Laplacian on Pseudo-Hermitian CR Manifolds (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we introduce a CR Cheeger constant and establish Cheeger-type and Buser-type inequalities for the first nonzero eigenvalue of the sub-Laplacian on compact strictly pseudoconvex pseudo-Hermitian CR manifolds. These results extend classical isoperimetric bounds from Riemannian to CR geometry. Applications are given to model examples, including the Heisenberg quotients, the standard CR sphere, and Rossi’s non-embeddable deformations.
Keywords: CR manifolds, Sub-Laplacian, Cheeger inequality, isoperimetric constant