Harnack inequalities on totally geodesic foliations with transverse Ricci flow

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.

Notes added and typos corrected

References in corpus (3)

• Generalized Bochner formulas and Ricci lower bounds for sub-Riemannian manifolds of rank two
• Weak solutions for the Ricci flow I
• Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation

Cited by in corpus (1)

• Sub-Riemannian Ricci curvature via generalized Gamma $z$ calculus