https://neckpinch.com/authors/qi-s-zhang/New arXiv papers by Qi S. Zhang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2509.14820arxiv:2509.14820Thu, 18 Sep 2025 00:00:00 GMTGang Tian, Qi S. Zhang, Zhenlei Zhang, Meng Zhu, Xiaohua Zhu — We first prove a uniform integral Laplace comparison result for the Kähler Ricci flow on Fano manifolds which depends only on the initial metric. As an application, using Cheeger-Colding theory and previous results by some of the authors, we give a direct and independent proof of the Hamilton-Tian conjecture on convergence of Kähler-Ricci flows, modulo a codimension 4 singular set. We also expounded on some existing literature on this conjecture.Ricci flowKähler–Ricci flow4-manifoldsKähler geometry https://arxiv.org/abs/2407.20719arxiv:2407.20719Tue, 30 Jul 2024 00:00:00 GMTQi S. Zhang — In this short survey paper, we first recall the log gradient estimates for the heat equation on manifolds by Li-Yau, R. Hamilton and later by Perelman in conjunction with the Ricci flow. Then we will discuss some of their applications and extensions focusing on sharp constants and improved curvature conditions.Ricci flowHarnack inequalities https://arxiv.org/abs/2406.17179arxiv:2406.17179Mon, 24 Jun 2024 00:00:00 GMTQi S. Zhang — Using a size condition of the sharp log Sobolev functional (log entropy) near infinity only, we prove a rigidity result for ancient Ricci flows without sign condition on the curvatures. The result is also related to the problem of identifying type II ancient Ricci flows and their backward limits.Ricci flowAncient solutionsSingularitiesPerelman entropyStability & uniqueness https://arxiv.org/abs/2306.10143arxiv:2306.10143Fri, 16 Jun 2023 00:00:00 GMTXiaolong Li, Qi S. Zhang — In this paper we prove matrix Li-Yau-Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply such estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature.Ricci flowHarnack inequalitiesHeat kernel