https://neckpinch.com/authors/yi-li/New arXiv papers by Yi Li, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2606.10354arxiv:2606.10354Tue, 09 Jun 2026 00:00:00 GMTChuanhuan Li, Yi Li — The analysis of singularities in scalar curvature is a classical problem. In this survey, we investigate the behavior of scalar curvature under several geometric flows, with a focus on three specific cases: the Ricci flow, the Kähler-Ricci flow coupled with (1,1)-forms, and the Laplacian flow.Ricci flowGeneralized & G₂ flowsSingularitiesKähler geometryScalar curvatureLong-time existence & convergence https://arxiv.org/abs/2604.02632arxiv:2604.02632Fri, 03 Apr 2026 00:00:00 GMTYi Li, Jie Wang, Pingsan Yuan, Chao Zheng — In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this curvature type, and establish an equivalent characterization of the problem, namely, the solution to the Calabi flow exists globally in time and converges if and only if there exists a weight function that realizes the prescribed curvature. In particular, for constant curvature weights, we prove that the solution to the Calabi flow exists globally in time and converges under certain topological conditions.Other curvature flowsKähler geometryKähler–Einstein & K-stabilityDiscrete & graph Ricci https://arxiv.org/abs/2310.14912arxiv: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://arxiv.org/abs/2205.07702arxiv: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