Calculus of Variations and Geometric Measure Theory

A. Hassannezhad - G. Kokarev

Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds

created by hassannezhad1 on 04 Dec 2020



Inserted: 4 dec 2020

Year: 2014

ArXiv: 1407.0358 PDF


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.