Parabolic frequency monotonicity for two nonlinear equations under Ricci flow
Differential Geometry
2025-04-30 v2 Analysis of PDEs
Abstract
In this paper, we consider the parabolic frequency for positive solutions of two nonlinear parabolic equations under the Ricci flow on closed manifolds. We obtain the monotonicity of parabolic frequency for the solution of two nonlinear parabolic equations with bounded Ricci curvature, then we apply the parabolic frequency monotonicity to get some integral type Harnack inequalities and we use -K1 instead of the lower bound 0 of Ricci curvature from Theorem 4.3 in 16, where K1 is any positive constant.
Cite
@article{arxiv.2310.14912,
title = {Parabolic frequency monotonicity for two nonlinear equations under Ricci flow},
author = {Chuanhuan Li and Yi Li and Kairui Xu and Jichun Zhu},
journal= {arXiv preprint arXiv:2310.14912},
year = {2025}
}
Comments
14 pages. accepted by Acta Mathematica Scientia