On Li-Yau gradient estimate for sum of squares of vector fields up to higher step
Differential Geometry
2016-02-05 v1
Abstract
In this paper, we generalize the Cao-Yau's gradient estimate for the sum of squares of vector fields up to higher step under assumption of the generalized curvature-dimension inequality. With its applications, by deriving a curvature-dimension inequality, we are able to obtain the Li-Yau gradient estimate for the CR heat equation in a closed pseudohermitian manifold of nonvanishing torsion tensors. As consequences, we obtain the Harnack inequality and upper bound estimate for the CR heat kernel.
Keywords
Cite
@article{arxiv.1602.01531,
title = {On Li-Yau gradient estimate for sum of squares of vector fields up to higher step},
author = {Der-Chen Chang and Shu-Cheng Chang and Chien Lin},
journal= {arXiv preprint arXiv:1602.01531},
year = {2016}
}
Comments
41 pages