  In this paper, we consider the class of uniformly locally univalent harmonic
mappings in the unit disk and build a relationship between its pre-Schwarzian
norm and uniformly hyperbolic radius. Also, we establish eight ways of
characterizing uniformly locally univalent sense-preserving harmonic mappings.
We also present some sharp distortions and growth estimates and investigate
their connections with Hardy spaces. Finally, we study subordination principles
of norm estimates.
