Classical minimal surfaces.


Scherk's surface
The catenoid. Discovered by L. Euler in 1740. The original name was allyside. The name catenoid is due to Plateau. The helicoid. Discovered by Meusnieur in 1776. Catalan characterized it as the only ruled nonflat minimal surface. The next minimal surface with helicoidal ends was discovered by Hoffman, Karcher and Wei 220 years later. Scherk's surfaces. In 1835, H. F. Scherk discovered 5 new minimal surfaces using a general representation for minimal surfaces by  Monge.
Enneper's surface A Riemann's surface
Enneper's surface. Constructed by Enneper in 1863, using his own  representation formulae. A singly periodic surface by Riemann. Riemann constructed a one-parametric family of properly embedded minimal surfaces, {Rl : l >0 }, which are invariant under a translation. This picture corresponds to R1. Schwarz' P surpace. The fundamental region is a tetrahedron which is 1/48 of a cube. The surface divides space into two congruent labyrinths.

Chen-Gackstätter's surfaces

Chen-Gackstatter surfaces. The first known examples with finite total curvature and genus greater than zero. Costa's surface. Constructed by C. Costa in 1981. Hoffman and Meeks gave the first proof of its embeddedness. It has the topology of a compact torus minus three points.  


 Mathematica 2.2 for Solaris.


Copyright: Francisco Martin.