Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures
Abstract
In this paper, we study the monotonicity of parabolic frequency motivated by frequency on RF 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-\'Emery 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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