论文标题
RICCI流动和RICCI谐波流的抛物线频率单调性具有有限曲线
Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures
论文作者
论文摘要
在本文中，我们研究了由\ cite {rf}频率{rf}的抛物线频率的单调性，而在ricci流动和歧管上的ricci-harmonic流动。在这里，我们考虑两种情况：一种是抛物线频率的抛物线频率的单调性，该方程用有界的bakry-émeryricci曲率解决方案，另一种情况是抛物线频率的单调性，用于使用有界RICCI曲率的热方程式解决方程。
In this paper, we study the monotonicity of parabolic frequency motivated by \cite{frequency on RF} under the Ricci flow and the Ricci-harmonic flow on manifolds. Here we consider two cases: one is the monotonicity of parabolic frequency for the solution of linear heat equation with bounded Bakry-Émery Ricci curvature, and another case is the monotonicity of parabolic frequency for the solution of heat equation with bounded Ricci curvature.
