The sharp lower bound for the first positive eigenvalue of a sub-Laplacian on a pseudo-Hermitian manifold

Li, Song-Ying; Luk, Hing-Sun

doi:10.1090/S0002-9939-03-07174-0

The sharp lower bound for the first positive eigenvalue of a sub-Laplacian on a pseudo-Hermitian manifold
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by Song-Ying Li and Hing-Sun Luk PDF

Proc. Amer. Math. Soc. 132 (2004), 789-798 Request permission

Abstract:

This paper studies, using the Bochner technique, a sharp lower bound of the first eigenvalue of a subelliptic Laplace operator on a strongly pseudoconvex CR manifold in terms of its pseudo-Hermitian geometry. For dimensions greater than or equal to $7$, the lower bound under a condition on the Ricci curvature and the torsion was obtained by Greenleaf. We give a proof for all dimensions greater than or equal to $5$. For dimension $3$, the sharp lower bound is proved under a condition which also involves a distinguished covariant derivative of the torsion.

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