Parabolic frequency monotonicity for two nonlinear equations under Ricci flow

Author:

Chuanhuan Li, Yi Li, Kairui Xu, Jichun Zhu

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Analysis of PDEs (math.AP)

journal:

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date:

2023-10-22 16:00:00

Abstract

In this paper, we consider the parabolic frequency for positive solutions of two nonlinear parabolic equations under the Ricci flow on closed manifolds. We obtain the monotonicity of parabolic frequency for the solution of two nonlinear parabolic equations with bounded Ricci curvature, then we apply the parabolic frequency monotonicity to get some integral type Harnack inequalities and we use -K1 instead of the lower bound 0 of Ricci curvature from Theorem 4.3 in 16, where K1 is any positive constant.