论文标题
标态曲率，熵和广义RICCI流动
Scalar curvature, entropy, and generalized Ricci flow
论文作者
论文摘要
我们为广义的RICCI流提供了一个加权标态曲率单调性公式的家族，涉及由重新规范化组流动动机的一定反应扩散方程演变而来的辅助DILATON场。这些标态曲率单调性是对新的Perelman型能量和熵单调性公式的双重双重性，通过与相关加权共轭热方程的溶液耦合。在RICCI流动的环境中，我们进一步获得了一个新的凸入纳什熵和伪端口原则的家族。
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.
