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.
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The author wishes to thank the anonymous referee for a careful reading of the manuscript and useful comments.
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Taheri, A. Gradient Estimates for a Weighted Γ-nonlinear Parabolic Equation Coupled with a Super Perelman-Ricci Flow and Implications. Potential Anal 59, 311–335 (2023). https://doi.org/10.1007/s11118-021-09969-2
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DOI: https://doi.org/10.1007/s11118-021-09969-2
Keywords
- Weighted Riemannian manifold
- Gradient estimates
- Super Perelman-Ricci flow
- Bakry-Émery tensor
- Harnack inequality
- Liouville theorem