On CR volume growth estimate in a complete pseudohermitian 3-manifold
Journal
International Journal of Mathematics
Journal Volume
25
Journal Issue
4
Date Issued
2014
Author(s)
Chang, T.-H.
Abstract
In this paper, we first derive the CR Reilly's formula and a CR Ricatti equation for sub-Laplacian of the Carnot–Carathéodory distance in a complete pseudohermitian 3-manifold. As a consequence, we obtain the CR volume growth estimate in a complete pseudohermitian 3-manifold under a lower bound of pseudohermitian curvature tensors. This is a generalization of Nagel, Stein and Wainger's volume growth estimate for the Heisenberg ball in the standard Heisenberg group.
SDGs
Type
journal article