The Harnack estimate for the Yamabe flow on CR manifolds of dimension 3
  We deform the contact form by the amount of the Tanaka-Webster curvature on a closed spherical $CR$ three-manifold. We show that if a contact form evolves with free torsion and positive Tanaka-Webster curvature as initial data, then a certain Harnack inequality for the Tanaka-Webster curvature holds. 
Shu-Cheng Chang and Jih-Hsin Cheng