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

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

2011-11-21

arxiv.org/abs/1111.5004v1

Mathematics

Differential Geometry

21 pages

Scientific paper

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.

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