https://neckpinch.com/authors/jichun-zhu/New arXiv papers by Jichun Zhu, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2310.14912/arxiv:2310.14912Mon, 23 Oct 2023 00:00:00 GMTChuanhuan Li, Yi Li, Kairui Xu, Jichun Zhu — 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.Ricci flowHarnack inequalities