Liouville theorems and elliptic gradient estimates for a nonlinear parabolic equation involving the Witten Laplacian
Ali Taheri
Abstract
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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>k</m:mi> <m:mo>,</m:mo> <m:mi>m</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> {(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.
Topics & Concepts
MathematicsRicci flowType (biology)Metric (unit)CurvatureNonlinear systemMathematical analysisLaplace operatorSpace (punctuation)Pure mathematicsMetric spaceRicci curvatureGeometryPhysicsLinguisticsPhilosophyBiologyQuantum mechanicsEcologyEconomicsOperations managementGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsGeometry and complex manifolds