Yongheng Han

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20232026

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6 papers · 1 filter

math.DG2026

Singularities of Mean Curvature Flow with Bounded Total Curvature

Yongheng 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_…

math.DG2026

The Covariant Riesz Transforms on Riemannian Manifolds

Yongheng Han, Bing Wang

We establish the $L^{p}$ -boundedness of the local covariant Riesz transform for differential forms on manifold $M$ with bounded $∥ R m ∥$ . Let $Δ_{j}$ be the Hodge Laplace operator on $…

math.DG2026

Well-posedness of mean curvature flow

Yongheng 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…

math.DG2026

The Calderón-Zygmund inequalities on evolving Riemannian manifolds

Yongheng Han, Bing Wang

The Calderón-Zygmund inequality is a cornerstone of harmonic analysis and partial differential equations. In this article, we establish various Calderón-Zygmund inequalities on evo…

math.DG2025

Singularities of mean curvature flow with bounded mean curvature and Morse index

Yongheng Han

We study the multiplicity of the singularities of mean curvature flow with bounded mean curvature and Morse index. For $3 \leq n \leq 6$ , we show that either the mean curvature or th…

math.DG2023

Ancient mean curvature flows from minimal hypersurfaces

Yongheng Han

For $n \geq 2$ , we construct $I$ -dimensional family of embedded ancient solutions to mean curvature flow arise from an unstable minimal hypersurface $Σ$ with finite total curvature…