Minimal Surfaces

The stable Bernstein theorem in $\mathbb{R}^{7}$
We give a Green-function proof of the stable Bernstein theorem in $\mathbb{R}^{7}$ for smooth, connected, complete, two-sided minimal …
Han Hong, Haizhong Li, Gaoming Wang
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Mixed Radial Volume Comparison under Spectral Ricci Bounds
Let $(M^n,g)$ be complete, let $u>0$, and assume $\operatorname{Ric}_g-\alpha\frac{\Delta_g u}{u}g\geq (n-1)\kappa g$. We introduce …
Han Hong, Gaoming Wang
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Stable Minimal Hypersurfaces in Positively Curved $4$-Manifolds
Let $M^3\to X^4$ be a complete, connected, two-sided stable minimal immersion. We prove that if the ambient sectional curvature is …
Han Hong, Gaoming Wang
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Regularity of branched stable minimal immersed hypersurfaces
We establish a sharp bound on the Hausdorff dimension of the non-branch singular set of branched stable minimal immersed hypersurfaces …
Gaoming Wang, Xuwen Zhang
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Spectral splitting theorem and ends of minimal hypersurfaces
In this paper, we give a new proof of the splitting theorem on manifolds with nonnegative spectral Ricci curvature proved in [APX24, …
Han Hong, Gaoming Wang
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Scalar curvature rigidity of domains in a 3-dimensional warped product
A warped product with a spherical factor and a logarithmically concave warping function satisfies a scalar curvature rigidity of the …
Xiaoxiang Chai, Gaoming Wang
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A splitting theorem for 3-manifold with nonnegative scalar curvature and mean-convex boundary
We show that a Riemannian 3-manifold with nonnegative scalar curvature and mean-convex boundary is flat if it contains an absolutely …
Han Hong, Gaoming Wang
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On $\delta$-Stable Minimal Hypersurfaces in $\mathbb{R}^{n+1}$
In this paper, we extend several results established for stable minimal hypersurfaces to $\delta$-stable minimal hypersurfaces. These …
Han Hong, Haizhong Li, Gaoming Wang
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Allard-Type Regularity for Varifolds with Prescribed Contact Angle
Given a bounded $C^2$ domain in $\mathbb{R}^{n+1}$ and an integral $n$-rectifiable varifold $V$ with bounded first variation and …
Gaoming Wang
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Dihedral rigidity in hyperbolic 3-space
We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by -6. The result …
Xiaoxiang Chai, Gaoming Wang
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