The first positive eigenvalue of the sub-laplacian on cr spheres

Amine Aribi; Ahmad El Soufi

The first positive eigenvalue of the sub-laplacian on cr spheres

Differential Geometry 2016-04-25 v1

Authors: Amine Aribi , Ahmad El Soufi

Abstract

We prove that the first positive eigenvalue, normalized by the volume, of the sub-Laplacian associated with a strictly pseudoconvex pseudo-Hermitian structure $\\theta$ on the CR sphere S 2n+1 $\subset$ C n+1 , achieves its maximum when $\\theta$ is the standard contact form.

Keywords

CR sphere sub-Laplacian first positive eigenvalue pseudo-Hermitian structure strictly pseudoconvex contact form eigenvalue estimate

Cite

@article{arxiv.1604.06453,
  title  = {The first positive eigenvalue of the sub-laplacian on cr spheres},
  author = {Amine Aribi and Ahmad El Soufi},
  journal= {arXiv preprint arXiv:1604.06453},
  year   = {2016}
}

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