Some Gradient Estimates and Liouville Properties of the Fast Diffusion Equation on Riemannian Manifolds
Wen Wang , Rulong Xie , Pan Zhang
Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (4) : 529 -550.
Some Gradient Estimates and Liouville Properties of the Fast Diffusion Equation on Riemannian Manifolds
In the paper, the authors provide a new proof and derive some new elliptic type (Hamilton type) gradient estimates for fast diffusion equations on a complete noncompact Riemannian manifold with a fixed metric and along the Ricci flow by constructing a new auxiliary function. These results generalize earlier results in the literature. And some parabolic type Liouville theorems for ancient solutions are obtained.
Gradient estimate / Fast diffusion equation / Ricci flow / Liouville theorem
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