Bounds for the first eigenvalue of the horizontal Laplacian in positively curved sub-Riemannian manifolds (Q1953084)

The authors establish lower bounds for the first nonzero eigenvalue of the natural geometric sub-elliptic Laplacian operator defined on sub-Riemannian manifolds of step 2 that satisfy a positive curvature condition. The methods are very general and can be applied even when the sub-Riemannian geometry has considerable torsion.