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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent Developments in Constant Mean Curvature Hypersurfaces
恒定 平均曲率 超曲面
2023/4/13
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.
The second pinching theorem for hypersurfaces with constant mean curvature in a sphere
Hypersurfaces with constant mean curvature Rigidity Scalar curvature Clifford torus
2011/1/20
We generalize the second pinching theorem for minimal hypersurfaces in a sphere due to Peng-Terng, Wei-Xu, Zhang, and Ding-Xin to the case of hypersurfaces with small constant mean curvature. Let Mn b...
Uniqueness of the Foliation of Constant Mean Curvature Spheres in Asymptotically Flat 3-Manifolds
Uniqueness Foliation of Constant Mean Curvature Spheres Asymptotically Flat 3-Manifolds
2011/2/21
In this paper I study the constant mean curvature surface in asymp-totically flat 3-manifolds with general asymptotics. Under some weak condition, I prove that outside some compact set in the asymptot...
Darboux transforms and simple factor dressing of constant mean curvature surfaces
Darboux transforms simple factor dressing constant mean curvature surfaces
2010/12/14
We define a transformation on harmonic maps N : M ! S2 from a Riemann surface M into the 2–sphere which depends on a parameter μ 2 C, the so–called μ–Darboux transformation.