Gradient estimates for a weighted Γ-nonlinear parabolic equation coupled with a super Perelman-Ricci flow and implications

Taheri, Ali (2021) Gradient estimates for a weighted Γ-nonlinear parabolic equation coupled with a super Perelman-Ricci flow and implications. Potential Analysis. ISSN 0926-2601

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Abstract

This article studies a nonlinear parabolic equation on a complete weighted manifold where the metric and potential evolve under a super Perelman-Ricci flow. It derives elliptic gradient estimates of local and global types for the positive solutions and exploits some of their implications notably to a general Liouville type theorem, parabolic Harnack inequalities and classes of Hamilton type dimension-free gradient estimates. Some examples and special cases are discussed for illustration.

Item Type: Article
Keywords: Weighted Riemannian manifold, gradient estimates, super Perelman-Ricci flow, Bakry-\'Emery tensor, Harnack inequality, Liouville theorem
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 18 Nov 2021 07:46
Last Modified: 26 Nov 2021 11:00
URI: http://sro.sussex.ac.uk/id/eprint/102953

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