Numerical computation of constant mean curvature surfaces using finite elements

Numerical computation of constant mean curvature surfaces using finite elements

This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle it is a flow like method in that it is linked to the gradient flow for the area functional, which gives reliable convergence properties. In the background a preconditioned conjugate gradie...

Surfaces of Constant Mean Curvature

New Constant Mean Curvature Surfaces

We use the DPW construction [5] to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points with a common tangent plane. An appendix, by the t...

Coplanar Constant Mean Curvature Surfaces

We consider constant mean curvature surfaces with finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors [GKS2, GKS1]. Here we extend the arguments to the case of an arbitrary number of ends, under the assumption that the asymptotic axes of the ends lie in a common plane...

Polyhedral Surfaces of Constant Mean Curvature

way, say, by assigning a length to each edge which fulÞlls the triangle identity on each triangle. In a locally Euclidean metric the distance between two points is measured along curves whose length is measured segment-wise on the open edges and triangles: DeÞnition 15 A curve γ on a simplicial complex M is called rectiÞable, if for every simplex σ ∈ M the part γ|σ is rectiÞable w.r.t. to the s...