English

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