Differential Harnack estimates for time-dependent heat equations with potentials in a closed spherical CR 3-manifold
In this paper, the author derives differential Harnack estimates for time-dependent heat equations with potentials under the CR Yamabe flow in a closed spherical CR 3-manifold with positive Tanaka-Webster curvature and vanishing torsion. It can be seen as a non-trivial generalization of Li-Yau-Hamilton inequality for the CR Yamabe flow. It is possible that this kind of Harnack estimate could play a central role in the study of the CR Yamabe flow. There are geometric quantities (for example the Tanaka-Webster scalar curvature) which satisfy the equation under the CR Yamabe flow in a closed CR 3-manifold. Indeed, these estimates could be used for understanding the singular models of positive Tanaka-Webster curvature under the CR Yamabe flow. In particular, this estimate should be useful in understanding the Yamabe solitons which one expects to model finite time singularities of the CR Yamabe flow.
scientific article; zbMATH DE number 7027386
scientific article