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arXiv · 2506.04937

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

Juanling Lu·Yu Zheng
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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.

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Juanling Lu, Yu Zheng. 2025-06-05. Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow. https://arxiv.org/abs/2506.04937

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