https://neckpinch.com/authors/kairui-xu/New arXiv papers by Kairui Xu, 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 https://neckpinch.com/papers/2205.07702/arxiv:2205.07702Mon, 16 May 2022 00:00:00 GMTChuanhuan Li, Yi Li, Kairui Xu — In this paper, we study the monotonicity of parabolic frequency motivated by 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.Ricci flowLimit spaces & RCD