A free boundary minimal surface in a domain 
is a minimal surface 
whose boundary lies on 
and which meets 
orthogonally. Equivalently,
in the calculus of variations it is a critical point of surface
area among variations which keep its boundary on
but allow the boundary to move there (Fraser and Schoen
2016).
The critical catenoid is the free boundary minimal surface in the unit ball 
having rotational symmetry.
