Scalar curvature, entropy, and generalized Ricci flow
Differential Geometry
2022-07-28 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2207.13197,
title = {Scalar curvature, entropy, and generalized Ricci flow},
author = {Jeffrey Streets},
journal= {arXiv preprint arXiv:2207.13197},
year = {2022}
}