Scalar Curvature, Entropy, and Generalized Ricci Flow
Jeffrey Streets
Abstract
Abstract We derive a family of weighted scalar curvature monotonicity formulas for generalized Ricci flow, involving an auxiliary dilaton field evolving by a certain reaction–diffusion equation motivated by renormalization group flow. These scalar curvature monotonicities are dual to a new family of Perelman-type energy and entropy monotonicity formulas by coupling to a solution of the associated weighted conjugate heat equation. In the setting of Ricci flow, we further obtain a new family of convex Nash entropies and pseudolocality principles.
Topics & Concepts
MathematicsRicci flowScalar curvatureRicci curvatureGeometric flowCurvature of Riemannian manifoldsCurvatureMonotonic functionMathematical physicsPrescribed scalar curvature problemRicci decompositionEntropy (arrow of time)Pure mathematicsMathematical analysisSectional curvatureGeometryPhysicsQuantum mechanicsGeometric Analysis and Curvature FlowsAdvanced Differential Geometry ResearchGeometry and complex manifolds