A Schwarz-Pick lemma for minimal maps

In this note, we prove a Schwarz-Pick type lemma for minimal maps between negatively curved Riemannian surfaces. More precisely, we prove that if $f:M \to N$ is a minimal map with bounded Jacobian between two complete negatively curved Riemann surfaces M and N whose sectional curvatures ${\sigma }_M$ and ${\sigma }_N$ satisfy $inf{\sigma }_M\ge sup{\sigma }_N$, then f is area decreasing.