  The minimal surface equation $Q$ in the second order contact bundle of $R^3$,
modulo translations, is provided with a complex structure and a canonical
vector-valued holomorphic differential form $Omega$ on $Q\0$. The minimal
surfaces $M$ in $R^3$ correspond to the complex analytic curves $C$ in $Q$,
where the derivative of the Gauss map sends $M$ to $C$, and $M$ is equal to the
real part of the integral of $\Omega$ over $C$. The complete minimal surfaces
of finite topological type and with flat points at infinity correspond to the
algebraic curves in $Q$.
