On the estimate of the first eigenvalue of a sublaplacian on a pseudohermitian 3-manifold
Journal
Pacific Journal of Mathematics
Journal Volume
232
Journal Issue
2
Pages
269-282
Date Issued
2007
Author(s)
Chiu, H.-L.
Abstract
In this paper, we study a lower bound estimate of the first positive eigenvalue of the sublaplacian on a three-dimensional pseudohermitian manifold.S.-Y.Li and H.-S. Luk derived the lower bound estimate under certain conditions for curvature tensors bounded below by a positive constant.By using the Li-Yau gradient estimate, we are able to get an effective lower bound estimate under a general curvature condition.The key is the discovery of a new CR version of the Bochner formula which involves the CR Paneitz operator.
Type
journal article