Is there a necessary relation between curvature and torsion of a closed non-intersecting curve on a minimal surface?
While playing with soap films I noted closed light threads migrating on a soap film in a certain way difficult to mathematically describe. I cannot imagine the motion is arbitrary. This can be also seen on solid surfaces catenoid surfaces if a string lying on it is displaced by hand.
EDIT1:
It may be in some way related to the Plateau / Rado problems.
