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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.
On complete constant mean curvature vertical multigraphs in E(κ,τ)
multigraphs constant mean curvature homogeneous spaces
2012/6/29
We prove that any complete surface with constant mean curvature in a homogeneous space E(\kappa,\tau) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a cons...
Caccioppoli's inequalities on constant mean curvature hypersurfaces in Riemannian manifolds
Caccioppoli’s inequality Simons’ equation constant mean curvature hypersurfaces stable finite index
2011/9/14
Abstract: We prove some Caccioppoli's inequalities for the traceless part of the second fundamental form of a complete, non compact, finite index, constant mean curvature hypersurface of a Riemannian ...
A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold
Asymptotically hyperbolic manifold Constraint equations Conformal method
2011/3/2
We construct solutions of the constraint equation with non constant mean curvature on an
asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain expo...
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...
Flows of constant mean curvature tori in the 3-sphere: The equivariant case
curvature tori the 3-sphere
2010/11/18
We present a deformation for constant mean curvature tori in the 3-sphere. We show that the moduli space of equivariant constant mean curvature tori in the 3-sphere is connected, and we classify the m...
Gauss maps of constant mean curvature surfaces in three-dimensional homogeneous spaces
Gauss maps of constant mean curvature surfaces three-dimensional homogeneous spaces
2010/11/26
It is well-known that for a surface in a 3-dimensional real space form the constancy of
the mean curvature is equivalent to the harmonicity of the Gauss map. However, this is not true
in general for...
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.
Links between different analytic descriptions of constant mean curvature surfaces
mean curvature math
2010/11/1
Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system \[ \begin{split} &\partial \psi_{1...