scholarly journals Upper bounds of Hessian matrix and gradient estimates of positive solutions to the nonlinear parabolic equation along Ricci flow

2022 ◽  
Vol 214 ◽  
pp. 112548
Author(s):  
Wen Wang
Keyword(s):  
Parabolic Equation ◽  
Positive Solutions ◽  
Ricci Flow ◽  
Nonlinear Parabolic Equation ◽  
Hessian Matrix ◽  
Upper Bounds ◽  
Gradient Estimates ◽  
Nonlinear Parabolic

scholarly journals Gradient Estimates for a Weighted Γ-nonlinear Parabolic Equation Coupled with a Super Perelman-Ricci Flow and Implications

2021 ◽  
Author(s):  
Ali Taheri
Keyword(s):  
Parabolic Equation ◽  
Ricci Flow ◽  
Nonlinear Parabolic Equation ◽  
Type Theorem ◽  
Gradient Estimates ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Harnack Inequalities ◽  
Nonlinear Parabolic ◽  
Special Cases

AbstractThis 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.

scholarly journals Liouville theorems and elliptic gradient estimates for a nonlinear parabolic equation involving the Witten Laplacian

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ali Taheri
Keyword(s):  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Gradient Estimates ◽  
Elliptic Type ◽  
Liouville Type ◽  
Witten Laplacian ◽  
Smooth Metric Measure Space ◽  
Nonlinear Parabolic ◽  
Global Estimates ◽  
Liouville Type Results

Abstract In this paper, we establish local and global elliptic type gradient estimates for a nonlinear parabolic equation on a smooth metric measure space whose underlying metric and potential satisfy a ( k , m ) {(k,m)} -super Perelman–Ricci flow inequality. We discuss a number of applications and implications including curvature free global estimates and some constancy and Liouville type results.

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