2023/07/08 by Xingyu Song, Ling Wu, Song, Xingyu +3 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2307.03879
openalex publication_date 2023/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Qi S.Zhang [26] has derived a sharp Li-Yau estimate for positive solutions of the heat equation on closed Riemannian manifolds with the Ricci curvature bounded below by a negative constant. The proof is based on an integral iteration argument which utilizes Hamilton's gradient estimate, heat kernel Gaussian bounds and parabolic Harnack inequality. In this paper, we show that the sharp Li-Yau estimate can actually be obtained directly following the classical maximum principle argument, which simplifies the proof in [26]. In addition, we apply the same idea to the heat and conjugate heat equations under the Ricci flow and prove some Li-Yau type estimates with optimal coefficients.