https://neckpinch.com/authors/ling-wu/New arXiv papers by Ling Wu, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2307.03879/arxiv:2307.03879Sat, 08 Jul 2023 00:00:00 GMTXingyu Song, Ling Wu, Meng Zhu — 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.Ricci flowHarnack inequalitiesHeat kernel https://neckpinch.com/papers/2211.14000/arxiv:2211.14000Fri, 25 Nov 2022 00:00:00 GMTLing Wu — Inspired by Hongjie Dong and Qi S. Zhang's article, we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain L^p spaces with p∈[2,+∞) and prove its analyticity with respect to time.Ricci solitonsLimit spaces & RCDBoundaries & non-compact