相关论文: Singularities of spacelike mean curvature one surf…

In this paper, firstly, we show the existence of a compact embedded constant mean curvature (CMC) hypersurface $\Sigma_1$ in $\mathbb{S}^{2n}$ of the type $S^{n-1} \times S^{n-1} \times S^{1}$. Moreover, the hypersurface $\Sigma_1$ exhibits…

Along cuspidal edge singularities on a given surface in Euclidean 3-space, which can be parametrized by a regular space curve, a unit normal vector field $\nu$ is well-defined as a smooth vector field of the surface. A cuspidal edge…

We review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.

In this paper, we describe a family of embedded hypersurfaces with constant mean curvature (CMC) in the $(n+1)$-dimensional unit sphere. In the process, we provide evidence for new CMC embedded examples. In particular, for some examples…

We investigate the close relationship between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. Just as in the case of minimal surfaces in Euclidean 3-space, the only complete connected…

We prove that any regular domain in Minkowski space is uniquely foliated by spacelike constant mean curvature (CMC) hypersurfaces. This completes the classification of entire spacelike CMC hypersurfaces in Minkowski space initiated by Choi…

We start the investigation of immersions $\Psi$ of a simply connected domain $D$ into three dimensional Euclidean space $R^3$, which have constant mean curvature (CMC-immersions), and allow for a group of automorphisms of $D$ which leave…

We give a global version of the Bryant representation of surfaces of constant mean curvature one (cmc-1) in hyperbolic space. This allows to set the associated non-abelian period problem in the framework of flat unitary vector bundles on…

We classify constant mean curvature surfaces invariant by a 1-parameter group of isometries in the Berger spheres and in the special linear group Sl(2, R). In particular, all constant mean curvature spheres in those spaces are described…

We investigate CMC-surfaces with periodic metric in a dressing orbit of the cylinder. It is shown, that such surfaces are always of finite type. Using the periodicity conditions for the extended frame of a CMC-surface, we develop an…

We define discrete constant mean curvature (cmc) surfaces in the three-dimensional Euclidean and Lorentz spaces in terms of sphere packings with orthogonally intersecting circles. These discrete cmc surfaces can be constructed from…

This paper continues the investigation of constant mean curvature (CMC) time functions in maximal globally hyperbolic spatially compact spacetimes of constant sectional curvature, which was started in math.DG/0604486. In that paper, the…

We prove that a spacelike spherical symmetric constant mean curvature (SSCMC) surface and a general spacelike constant mean curvature (CMC) surface with certain boundary condition at the future null-infinity in Schwarzschild spacetime are…

It is classically known that a real cubic surface in the real projective 3-space cannot have more than one solitary point (locally given by x^2+y^2+z^2=0) whereas it can have up to four nodes (x^2+y^2-z^2=0). We show that on any surface of…

We review recent results on classifying complete constant mean curvature 1 (CMC 1) surfaces in hyperbolic 3-space with low total curvature. There are two natural notions of "total curvature" -- one is the total absolute curvature, which is…

In this paper we prove that the only algebraic constant mean curvature (cmc) surfaces in R^3 of order less than four are the planes, the spheres and the cylinders. The method used heavily depends on the efficiency of algorithms to compute…

Anti-de Sitter space is the Lorentzian space form with negative curvature. In this paper we consider lightlike hypersurfaces along spacelike submanifolds in anti-de Sitter space with general codimension. In particular, we investigate the…

We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space $\real^{2,1}$. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC…

For constant mean curvature surfaces of class $C^2$ immersed inside Sasakian sub-Riemannian 3-manifolds we obtain a formula for the second derivative of the area which involves horizontal analytical terms, the Webster scalar curvature of…

A surface of constant mean curvature (CMC) equal to $H$ in a sub-Riemannian $3$-manifold is strongly stable if it minimizes the functional $\text{area}+2H\,\text{volume}$ up to second order. In this paper we obtain some criteria ensuring…