Some Mathematical Images - David Brander
Spherical SurfacesSurfaces with constant positive Gauss curvature. These surfaces are produced using loop group methods, described here: Spherical surfaces |
Symmetric |
More examples |
Pseudospherical Surfaces with singularitiesSurfaces with constant negative Gauss curvature and prescribed singularities. These surfaces are produced by solving the singular geometric Cauchy problem. |
Set 1 |
Degenerate |
Planar curves |
Parameter lines |
Willmore SurfacesWillmore surfaces are local minimizers of the Willmore energy $\int_S H^2 dA$, where $H$ is the mean curvature. This energy minimizing property makes the surfaces appear very smooth and natural. The images here are produced using an implementation of our solution of a generalization of Björling's problem to these surfaces. Read more... |
Equivariant |
Rotational |
Profiles |
More Images |
Pseudospherical SurfacesSurfaces with constant negative Gauss curvature. The surfaces shown here each contain a well-known curve as a principal geodesic curve. They are produced using the solution of the geometric Cauchy problem given by M. Svensson and myself in J. Differential Geom. 93, (2013), 37-66. Read more... |
Parabola |
Ellipse |
Lemniscate |
Cubic |
CMC Deformations of Minimal SurfacesThese images show some examples of non-minimal CMC surfaces produced from famous minimal surfaces, using a natural deformation given in this article , which is joint work with J.F. Dorfmeister. Read more... |
Catenoid |
Helicoid |
Enneper Surface |
Scherk Surface |
Singularities of SurfacesGeneric, or stable, singularities are those which persist under small local deformations of the surface through surfaces of the same class. Some of my work has been on the singularities of CMC surfaces in $2+1$-dimensional space-time. |
Generic |
Branch Points |
Spacelike CMC |
Surfaces foliated by Euler elasticaThe elastica are curves that minimize bending energy. These were studied and classified by Bernoulli and Euler. Here are some images of surfaces swept out in space by (varying) elastica. |
All Euler Elastica |
Roughly rotational |
More examples |
Freeform |