Let be a continuous norm in , i.e., is a nonnegative, convex, homogeneous function on . Let be a closed, connected, rectifiable curve parametrized by the arc length , and set
We say that is in equilibrium if for all smooth variations , preserving the area enclosed by , the derivative of is initially nonnegative.
The Wulff shape of is the boundary of the unit ball in the dual norm of . It is known that, for a given , among all curves enclosing the same area, the boundary of the ball (the Wulff shape) minimizes ; here is the unit normal of . The main result of this paper is that, for any continuous norm on , an equilibrium, closed, connected curve must be a (scaled) Wulff shape (possibly with integer multiplicity if nonembedded curves are allowed).