Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow
Differential Geometry
2025-06-06 v1
Abstract
In this paper, we establish Li-Yau-type and Hamilton-type estimates for positive solutions to the heat equation associated with the generalized Ricci flow, under a less stringent curvature condition. Compared with [25] and [35], these estimates generalize the results in Ricci flow to this new flow under the weaker Ricci curvature bounded assumption. As an application, we derive the Harnack-type inequalities in spacetime and find the monotonicity of one parabolic frequency for positive solutions of the heat equation under bounded Ricci curvature.
Keywords
Cite
@article{arxiv.2506.04937,
title = {Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow},
author = {Juanling Lu and Yu Zheng},
journal= {arXiv preprint arXiv:2506.04937},
year = {2025}
}