What are the possible shapes of various things and why?
For instance, when a closed wire or a frame is dipped into a soap solution
and is raised up from the solution, the surface spanning the wire is a soap
film. What are the possible shapes of soap films and why? Or, for instance, why
is DNA like a double spiral staircase? ``What..?'' and ``why..?'' are
fundamental questions, and when answered, help us understand the world we live
Soap films, soap bubles, and surface tension were extensively studied by the
Belgian physicist and inventor (the inventor of the stroboscope) Joseph Plateau
in the first half of the nineteenth century. At least since his studies, it has
been known that the right mathematical model for soap films are minimal
surfaces -- the soap film is in a state of minimum energy when it is covering
the least possible amount of area.
We will discuss here the answer to the question: ``What are the possible
shapes of embedded minimal disks in $\RR^3$ and why?''.