https://neckpinch.com/authors/yongheng-han/New arXiv papers by Yongheng Han, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.18197arxiv:2610.18197Tue, 13 Oct 2026 00:00:00 GMTYongheng Han, Zhen Wang — We prove that every tangent flow at the first singular time of a smooth, closed, embedded mean curvature flow has smooth support, provided that the total curvature satisfies sup_(t∈[0,T))∫_(Mₜ)|A|ⁿ dμₜ<∞. This extends Ilmanen's smoothness result for tangent flows to higher dimensions.Mean curvature flowSingularities https://arxiv.org/abs/2603.22809arxiv:2603.22809Tue, 24 Mar 2026 00:00:00 GMTYongheng Han — In this paper, using heat kernel estimates and contraction mapping principle, we give a new proof of the existence and uniqueness of mean curvature flow starting from hypersurface with bounded second fundamental form. Moreover, we show the continuous dependence of mean curvature flow on initial data.Mean curvature flowHeat kernelStability & uniqueness https://arxiv.org/abs/2501.05489arxiv:2501.05489Thu, 09 Jan 2025 00:00:00 GMTYongheng Han — We study the multiplicity of the singularities of mean curvature flow with bounded mean curvature and Morse index. For 3≤ n≤ 6, we show that either the mean curvature or the Morse index blows up at the first singular time for a closed smooth embedded mean curvature flow in ℝⁿ⁺¹.Mean curvature flowSingularities https://arxiv.org/abs/2311.15278arxiv:2311.15278Sun, 26 Nov 2023 00:00:00 GMTYongheng Han — For n≥ 2, we construct I-dimensional family of embedded ancient solutions to mean curvature flow arise from an unstable minimal hypersurface Σ with finite total curvature in ℝⁿ⁺¹, where I is the Morse index of the Jacobi operator on Σ.Mean curvature flowAncient solutionsStability & uniquenessMinimal & CMC surfaces