Related papers: Constant Mean Curvature Trinoids

We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\gamma}}$ for $|X|$ large, when $A<0$ and…

We study constant mean curvature graphs in the Riemannian 3-dimensional Heisenberg spaces ${\cal H}={\cal H}(\tau)$. Each such ${\cal H}$ is the total space of a Riemannian submersion onto the Euclidean plane $\mathbb{R}^2$ with geodesic…

A transformation based on mean curvature is introduced which morphs triangulated surfaces into round spheres.

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 study the rigidity of complete, embedded constant mean curvature surfaces in R^3. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R^3 or its…

It is shown that the equation which describes constant mean curvature surface via the generalized Weierstrass-Enneper inducing has Hamiltonian form. Its simplest finite-dimensional reduction has two degrees of freedom, integrable and its…

We show that one-sided Alexandrov embedded constant mean curvature cylinders of finite type in the 3-sphere are surfaces of revolution. This confirms a conjecture by Pinkall and Sterling that the only embedded constant mean curvature tori…

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…

In hyperbolic 3-space $\mathbb{H}^3$ surfaces of constant mean curvature $H$ come in three types, corresponding to the cases $0 \leq H < 1$, $H = 1$, $H > 1$. Via the Lawson correspondence the latter two cases correspond to constant mean…

We combine the DPW method and Opening Nodes to construct embedded surfaces of positive constant mean curvature with Delaunay ends in euclidean space, with no limitation to the genus or number of ends.

We describe the curves of constant (geodesic) curvature and torsion in the three-dimensional round sphere. These curves are the trajectory of a point whose motion is the superposition of two circular motions in orthogonal planes. The global…

Motivated by the large ammount of results obtained for minimal and positive constant mean curvature surfaces in several ambient spaces, the aim of this paper is to obtain half-space theorems for properly immersed surfaces in $\mathbb{R}^3$…

In this paper we study horizontal curvatures for surfaces embedded in three-dimensional contact sub-Riemannian Lie groups. Using a Riemannian approximation scheme, we derive explicit formulas for horizontal Gauss curvature, horizontal mean…

The generalization of (super)integrable Euclidean classical Hamiltonian systems to the two-dimensional sphere and the hyperbolic space by preserving their (super)integrability properties is reviewed. The constant Gaussian curvature of the…

The isotropic 3-space I^3 which is one of the Cayley--Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we give several classifications on the…

We give the classification of constant mean curvature rotational surfaces of elliptic, hyperbolic, and parabolic type in the four-dimensional pseudo-Euclidean space with neutral metric.

In this paper, we establish a geometric correspondence between constant curvature one metrics with two conical singularities on $S^{2}$ and isometric immersions into Euclidean 3-space $\mathbb{E}^{3}$. Specifically, we explicitly construct…

A study of the generalized Weierstrass system which can be used to induce mean curvature surfaces in three-dimensional Euclidean space is presented.

We show existence of constant mean curvature 1 surfaces in both hyperbolic 3-space and de Sitter 3-space with two complete embedded ends and any positive genus up to genus twenty. We also find another such family of surfaces in de Sitter…

We prove that a totally umbilical biharmonic surface in any $3$-dimensional Riemannian manifold has constant mean curvature. We use this to show that a totally umbilical surface in Thurston's 3-dimensional geometries is proper biharmonic if…