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On li-yau gradient estimate for sum of squares of vector fields up to higher step

Der-Chen Chang Georgetown University Shu-Cheng Chang National Taiwan University Chien Lin National Tsing-Hua University

Differential Geometry mathscidoc:1611.10001

to appear in CAG
In this paper, we generalize the Cao-Yau'’s gradient estimate for the sum of squares of vector …elds up to higher step under ssumption 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. 1.
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@inproceedings{der-chenon,
  title={ON LI-YAU GRADIENT ESTIMATE FOR SUM OF SQUARES OF VECTOR FIELDS UP TO HIGHER STEP},
  author={Der-Chen Chang, Shu-Cheng Chang, and Chien Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161101095852339681603},
  booktitle={to appear in CAG},
}
Der-Chen Chang, Shu-Cheng Chang, and Chien Lin. ON LI-YAU GRADIENT ESTIMATE FOR SUM OF SQUARES OF VECTOR FIELDS UP TO HIGHER STEP. In to appear in CAG. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161101095852339681603.
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