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

Abstract

We establish lower bounds for the first non-zero eigenvalue for 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.

arXiv comment21 pages

Cited by in corpus (1)

• Sobolev, Poincare and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality