Han Hong

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20242026

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6 papers · 1 filter

math.DG2026

Stable Free Boundary Minimal Hypersurfaces in $B^{5}$ and $B^{6}$

Han Hong, Yujie Wu

In this paper, we prove that there is no complete two-sided stable immersed free boundary minimal hypersurface in the closed Euclidean unit ball $B^{n + 1}$ for $n \leq 5$ .

math.DG2026

Homological $k$ -systole in $n$ -manifolds with positive intermediate curvature

Jingche Chen, Han Hong

In this paper, we prove optimal $k$ -systolic inequalities and characterize the case of equality on closed $n$ -dimensional Riemannian manifolds with positive intermediate curvature…

math.DG2025

Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary

Jingche Chen, Han Hong

We establish curvature obstruction theorems for manifolds with boundary. Our main theorems show that, for dimensions up to 7, a topologically nontrivial compact manifold with bound…

math.DG2025

Do Carmo's problem for CMC hypersurfaces in $R^{6}$

Jingche Chen, Han Hong, Haizhong Li

In this paper, we prove that complete noncompact constant mean curvature hypersurfaces in $R^{6}$ with finite index must be minimal. This provides a positive answer to do Ca…

math.DG2024

Curvature estimates for semi-convex solutions of asymptotic Plateau problem in $H^{n + 1}$

Han Hong, Ruijia Zhang

In this paper, we consider the asymptotic $σ_{k}$ Plateau problem in hyperbolic space. We establish $C^{2}$ estimates for semi-convex complete hypersurfaces satisfying constant $σ_{k}$ c…

math.DG2024

Rigidity of CMC hypersurfaces in 5-and 6-manifolds

Han Hong, Zetian Yan

We prove that nonnegative $3$ -intermediate Ricci curvature combined with uniformly positive $k$ -triRic curvature implies rigidity of complete noncompact two-sided stable minimal hy…

Stable Free Boundary Minimal Hypersurfaces in B5 and B6

Homological k-systole in n-manifolds with positive intermediate curvature