https://neckpinch.com/authors/meng-zhu/New arXiv papers by Meng Zhu, 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/2307.03879arxiv: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://arxiv.org/abs/2304.01453arxiv:2304.01453Tue, 04 Apr 2023 00:00:00 GMTHuai-Dong Cao, Meng Zhu — In this paper, we continue investigating the second variation of Perelman's ν-entropy for compact shrinking Ricci solitons. In particular, we improve some of our previous work in "H.-D. Cao and M. Zhu, Math. Ann. 353 (2012), No. 3, 747-763", as well as the more recent work in "M. Mehrmohamadi and A. Razavi, arXiv:2104.08343", and obtain a necessary and sufficient condition for a compact shrinking Ricci soliton to be linearly stable. Our work also extends similar results of Hamilton, Ilmanen and the first author in "arXiv:math.DG/0404165" (see also "H.-D. Cao and C. He, J. Reine Angew. Math. 2015 (2015), no. 709, 229-246.") for positive Einstein manifolds to the compact shrinking Ricci soliton case.Ricci solitonsEinstein metricsStability & uniqueness