Harnack estimates for nonlinear backward heat equations in geometric flows

摘要

Let M be a closed Riemannian manifold with a family of Riemannian metrics g(ij)(t) evolving by a geometric flow partial derivative(t)g(ij) = -2S(ij), where S-ij (t) is a family of smooth symmetric two-tensors. We derive several differential Harnack estimates for positive solutions to the nonlinear backward heat-type equation