Decouplings for surfaces of zero curvature

Decouplings for Curves

Curvature Estimation for Segmentation of Triangulated Surfaces

An important aspect of reverse engineering is the production of digital representations of physical objects for CAD systems. The first stage involves taking 3D coordinate measurements for points on the surface of the object and producing in general an unstructured set of points, called a point cloud. A triangulated surface can be generated from such a point cloud, allowing copies of the origina...

Computing lines of curvature for implicit surfaces

Article history: Received 13 August 2008 Received in revised form 2 July 2009 Accepted 13 July 2009 Available online 16 July 2009

Classification of Embedded Constant Mean Curvature Surfaces with Genus Zero and Three Ends

For each embedded constant mean curvature surface in R 3 with three ends and genus zero, we construct a conjugate cousin boundary contour in S 3. The moduli space of such contours is parametrized by the space of triples of distinct points in S 2. This imposes necessary conditions on the cmc surfaces; moreover, we expect the space of triples exactly parametrizes their moduli space. Our approach ...

Relative parabolicity of zero mean curvature surfaces in R 3 and R 31

If the Lorentzian norm on a maximal surface in the 3-dimensional Lorentz-Minkowski space R 1 is positive and proper, then the surface is relative parabolic. As a consequence, entire maximal graphs with a closed set of isolated singularities are relative parabolic. Furthermore, maximal and minimal graphs over closed starlike domains in R 1 and R, respectively, are relative parabolic.