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- Title
Scalar Curvature, Entropy, and Generalized Ricci Flow.
- Authors
Streets, Jeffrey
- 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.
- Subjects
CURVATURE; RENORMALIZATION group; ENTROPY; RENORMALIZATION (Physics); HEAT equation; REACTION-diffusion equations; DILATON; RICCI flow
- Publication
IMRN: International Mathematics Research Notices, 2023, Vol 2023, Issue 11, p9481
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad002