Parabolic Frequency Monotonicity on Ricci Flow and Ricci-Harmonic Flow with Bounded Curvatures

被引：0
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作者：
Chuanhuan Li
Yi Li
Kairui Xu
机构：
[1] Beijing Normal University,School of Mathematical Sciences
[2] Southeast University,School of Mathematics and Shing
[3] Southeast University,Tung Yau Center of Southeast University
来源：
The Journal of Geometric Analysis | 2023年 / 33卷
关键词：
Parabolic frequency; Ricci flow; Ricci-harmonic flow; 58J35; 58J90; 35R01; 53E20;
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摘要：
In this paper, we study the monotonicity of parabolic frequency motivated by Baldauf and Kim (Parabolic frequency on Ricci flows. To appear in Int. Math. Res. Not., rnac128. https://doi.org/10.1093/imrn/rnac128) 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-Émery Ricci curvature, and another case is the monotonicity of parabolic frequency for the solution of heat equation with bounded Ricci curvature.
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