6 papers
Regularity of branched stable minimal immersed hypersurfaces
Gaoming Wang, Xuwen Zhang
We establish a sharp bound on the Hausdorff dimension of the non-branch singular set of branched stable minimal immersed hypersurfaces whose singular sets have locally finite $\mat…
Spectral splitting theorem and ends of minimal hypersurfaces
Han Hong, Gaoming Wang
In this paper, we give a new proof of the splitting theorem on manifolds with nonnegative spectral Ricci curvature proved in [APX24, CMMR24, HW26]. Furthermore, by constructing wei…
Regularity of stable capillary minimal hypersurfaces
Gaoming Wang, Xuwen Zhang
We develop a regularity and compactness theory for stable capillary minimal hypersurfaces in the half-space with contact angle and dimension $n \geq…
A splitting theorem for manifolds with spectral nonnegative Ricci curvature and mean-convex boundary
Han Hong, Gaoming Wang
We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension has $λ_1(-αÎ+\ope…
Scalar curvature rigidity of domains in a 3-dimensional warped product
Xiaoxiang Chai, Gaoming Wang
A warped product with a spherical factor and a logarithmically concave warping function satisfies a scalar curvature rigidity of the Llarull type. We develop a scalar curvature rig…
A splitting theorem for 3-manifold with nonnegative scalar curvature and mean-convex boundary
Han Hong, Gaoming Wang
We show that a Riemannian 3-manifold with nonnegative scalar curvature and mean-convex boundary is flat if it contains an absolutely area-minimizing (in the free boundary sense) ha…