  We prove the existence of $C^{1,1}$ isometric immersions of several classes
of metrics on surfaces $(\mathcal{M},g)$ into the three-dimensional Euclidean
space $\mathbb{R}^3$, where the metrics $g$ have strictly negative curvature.
These include the standard hyperbolic plane, generalised helicoid-type metrics
and generalised Enneper metrics. Our proof is based on the method of
compensated compactness and invariant regions in hyperbolic conservation laws,
together with several observations on the geometric quantities (Gauss
curvature, metric components etc.) of negatively curved surfaces.
