Scalar Curvature, Entropy, and Generalized Ricci Flow
Scalar Curvature, Entropy, and Generalized Ricci Flow
复制标题
DOI：
10.1093/imrn/rnad002
复制
发表时间：
2022-07
影响因子：
1
通讯作者：
J. Streets
中科院分区：
文献类型：
--
作者：
J. Streets
我们推导了一类广义Ricci流的加权标量曲率单调性公式，其中包含由重整化群流驱动的反应扩散方程演化的辅助Ricci子场.这些标量曲率的单调性是对偶的一个新的家庭的佩雷尔曼型的能量和熵的单调性公式，通过耦合到相关的加权共轭热方程的解决方案。在Ricci流的背景下，我们进一步得到了一族新的凸Nash熵和伪局部性原理。
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.