What function describes the minimal surface of this object?
The object consists of four circular arcs glued together. One arc is parallell to another arc, and a third arc is parallell to a fourth arc. The first two arcs are orthogonal to the other two arcs. But anyways, the picture explains it better, so don't trust my words too much. The arcs are half circles.
With four discontinuities on the curve, the spanning film will have singularities too.
A continuous space curve like the "Tennis-ball curve" : http://thatsmaths.com/2014/05/29/the-high-power-hypar/ can be better handled I guess.
To find the minimal surface we have to set up pdes like in the Rado's or Plateau's problems...bit cumbersome.
Interesting reading I enjoyed was: " Science of soap bubbles & films" by Cyril Isenberg.
$x^2+y^2\le a^2,~z=a,~z=-a$ for $x\ge 0, y\ge 0$ and $y^2+z^2\le a^2,~x=a,~x=-a$ for $z\ge 0, y< 0$
I don't know how is to define this set as a function $f(x,y,z)=0$.
– Alexander Vigodner Aug 13 '14 at 18:32Am I correct with inequalities?