https://neckpinch.com/authors/xiaolong-li/New arXiv papers by Xiaolong Li, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2307.10920arxiv:2307.10920Thu, 20 Jul 2023 00:00:00 GMTXiaolong Li, Hao-Yue Liu, Xin-An Ren — We prove matrix Li-Yau-Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Kähler-Ricci flow. As an application, we obtain a monotonicity formula.Ricci flowKähler–Ricci flowHarnack inequalitiesHeat kernelKähler geometry 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 https://arxiv.org/abs/2303.17663arxiv:2303.17663Thu, 30 Mar 2023 00:00:00 GMTHarry Fluck, Xiaolong Li — This article aims to understand the behavior of the curvature operator of the second kind under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature operator of the second kind explicitly in terms of that of the curvature operator (of the first kind). Second, we prove that a-positive/a-nonnegative curvature operator of the second kind is preserved by the Ricci flow in dimension three for all a ∈ [1,5].Ricci flow3-manifoldsEigenvalues & spectrum