  We investigate the two-word Naming Game on two-dimensional random geometric
graphs. Studying this model advances our understanding of the spatial
distribution and propagation of opinions in social dynamics. A main feature of
this model is the spontaneous emergence of spatial structures called opinion
domains which are geographic regions with clear boundaries within which all
individuals share the same opinion. We provide the mean-field equation for the
underlying dynamics and discuss several properties of the equation such as the
stationary solutions and two-time-scale separation. For the evolution of the
opinion domains we find that the opinion domain boundary propagates at a speed
proportional to its curvature. Finally we investigate the impact of committed
agents on opinion domains and find the scaling of consensus time.
