Geodesic spaces of low Nagata dimension

We show that every geodesic metric space admitting an injective continuous map into the plane as well planar graph has Nagata dimension at most two, hence asymptotic two. This relies on and answers a question in recent work by Fujiwara Papasoglu. conclude all three-dimensional Hadamard manifolds have three. As consequence, such are absolute Lipschitz retracts.