Helicoids of constant mean curvature and their Gauss maps

Gauss Maps of the Mean Curvature Flow

Let F : Σ n × [0, T) → R n+m be a family of compact immersed submanifolds moving by their mean curvature vectors. We show the Gauss maps γ : (Σ n , g t) → G(n, m) form a harmonic heat flow with respect to the time-dependent induced metric g t. This provides a more systematic approach to investigating higher codimension mean curvature flows. A direct consequence is any convex function on G(n, m)...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Notes on Constant Mean Curvature Surfaces and Their Graphical Presentation

In this paper graphical presentation some of the constant mean curvature surfaces (CMC surfaces) is given. This work is an extension of the results [3]. Interesting shapes and complicate structures of CMC surfaces obtained using Mathematica computer program are given.

On semidiscrete constant mean curvature surfaces and their associated families

The present paper studies semidiscrete surfaces in three-dimensional Euclidean space within the framework of integrable systems. In particular, we investigate semidiscrete surfaces with constant mean curvature along with their associated families. The notion of mean curvature introduced in this paper is motivated by a recently developed curvature theory for quadrilateral meshes equipped with un...

Discrete Constant Mean Curvature Surfaces and Their Index

We define triangulated piecewise linear constant mean curvature surfaces using a variational characterization. These surfaces are critical for area amongst continuous piecewise linear variations which preserve the boundary conditions, the simplicial structures, and (in the nonminimal case) the volume to one side of the surfaces. We then find explicit formulas for complete examples, such as disc...