# Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds

Research output: Contribution to journalArticle (Academic Journal)peer-review

## Abstract

We study eigenvalue problems for intrinsic sub-Laplacians on regular sub-Riemannian manifolds. We prove upper bounds for sub-Laplacian eigenvalues $\lambda_k$ of conformal sub-Riemannian metrics that are asymptotically sharp as $k\to+\infty$. For Sasakian manifolds with a lower Ricci curvature bound, and more generally, for contact metric manifolds conformal to such Sasakian manifolds, we obtain eigenvalue inequalities that can be viewed as versions of the classical results by Korevaar and Buser in Riemannian geometry.
Original language English 1049–1092 Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16 4 21 Dec 2016 https://doi.org/10.2422/2036-2145.201409_005 E-pub ahead of print - 21 Dec 2016

## Keywords

• sub-Laplacian
• eigenvalue bounds
• sub-Riemannian manifold
• Sasakian manifold

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