Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures
Differential Geometry
2023-09-06 v1
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-\'{E}mery Ricci curvature, and another case is the monotonicity of parabolic frequency for the solution of heat equation with bounded Ricci curvature.
Keywords
Cite
@article{arxiv.2205.07702,
title = {Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures},
author = {Chuanhuan Li and Yi Li and Kairui Xu},
journal= {arXiv preprint arXiv:2205.07702},
year = {2023}
}
Comments
16 pages