English

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