Gradient Estimates for a Weighted Γ-nonlinear Parabolic Equation Coupled with a Super Perelman-Ricci Flow and Implications
Ali Taheri
Abstract
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.
Topics & Concepts
Ricci flowMathematicsHarnack's inequalityHarnack's principleBalanced flowNonlinear systemMathematical analysisType (biology)Metric (unit)Manifold (fluid mechanics)Flow (mathematics)Potential theoryDimension (graph theory)Ricci curvaturePure mathematicsGeometryPhysicsBiologyMechanical engineeringCurvatureEcologyQuantum mechanicsEconomicsOperations managementEngineeringGeometric Analysis and Curvature FlowsGeometry and complex manifoldsNonlinear Partial Differential Equations