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.

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Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (4) : 529 -550. DOI: 10.1007/s11401-021-0276-3
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Some Gradient Estimates and Liouville Properties of the Fast Diffusion Equation on Riemannian Manifolds

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Abstract

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.

Keywords

Gradient estimate / Fast diffusion equation / Ricci flow / Liouville theorem

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Wen Wang, Rulong Xie, Pan Zhang. Some Gradient Estimates and Liouville Properties of the Fast Diffusion Equation on Riemannian Manifolds. Chinese Annals of Mathematics, Series B, 2021, 42(4): 529-550 DOI:10.1007/s11401-021-0276-3

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