The differential equation $\Delta x=2H(x\sb{u}\wedge x\sb{v})$ with vanishing boundary values
Henry C. Wente · Proceedings of the American Mathematical Society · 1975
If $x(u,v)$ is a solution to the system $\Delta x = 2H({x_u} \wedge {x_v})$ on a bounded domain $G \subset {R^2}$ with finite Dirichlet integral and with $x = 0$ on $\partial G$, then $x \equiv 0$ for simply connected $G$, but for doubly-connected $G$ we construct nontrivial solutions.