Hamilton type gradient estimates for a general type of nonlinear parabolic equations on Riemannian manifolds

Abstract

$ (\Delta_{V}-q(x, t)-\partial_{t})u(x, t) = A(u(x, t)) $ on complete Riemannian manifold (with fixed metric). When $ V = 0 $ and the metric evolves under the geometric flow, we also derive some Hamilton type gradient estimates. Finally, as applications, we obtain some Liouville type theorems of some specific parabolic equations.

Keywords

• parabolic equation
• gradient estimate
• liouville type theorem
• geometric flow
• curvature