Harnack inequalities on totally geodesic foliations with transverse Ricci flow
Differential Geometry
2018-07-31 v2
Abstract
In the current paper,under the transverse Ricci flow on a totally geodesic Riemannian foliation, we prove two types of differential Harnack inequalities (Li-Yau gradient estimate) for the positive solutions of the heat equation associated with the time dependent horizontal Laplacian operators. We also get a time dependent version of the generalized curvature dimension inequality. As a consequence of aforementioned results, we also get parabolic Harnack inequalities and heat kernel upper bounds.
Keywords
Cite
@article{arxiv.1712.02275,
title = {Harnack inequalities on totally geodesic foliations with transverse Ricci flow},
author = {Qi Feng},
journal= {arXiv preprint arXiv:1712.02275},
year = {2018}
}
Comments
Notes added and typos corrected