Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures
arXiv:2205.07702 · doi:10.1007/s12220-023-01345-3
Abstract
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.
arXiv comment16 pages