Abstract:
The sub-Laplacian plays a key role in CR geometry.
In this paper, we investigate eigenvalues of the sub-Laplacian on bounded domains of
strictly pseudoconvex CR manifolds, strictly pseudoconvex CR manifolds submersed in
Riemannian manifolds.
We establish some Levitin–Parnovski-type inequalities and Cheng–Huang–Wei-type
inequalities for their eigenvalues.
As their applications, we derive some results for the standard CR sphere
$\mathbb{S}^{2n+1}$
in
$\mathbb{C}^{n+1}$,
the Heisenberg group
$\mathbb{H}^n$,
a strictly
pseudoconvex CR manifold submersed in a minimal submanifold in
$\mathbb{R}^m$,
domains of
the standard sphere
$\mathbb{S}^{2n}$
and the projective space
$\mathbb{F}P^m$.
