Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow

TL;DR

This paper extends classical heat equation estimates to solutions under generalized Ricci flow with weaker curvature assumptions, deriving new inequalities and monotonicity results.

Contribution

It introduces Li-Yau and Hamilton-type estimates for heat solutions under generalized Ricci flow with less restrictive curvature conditions.

Findings

Established Li-Yau-type estimates for positive solutions.

Proved Harnack inequalities in spacetime.

Demonstrated monotonicity of parabolic frequency.

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.