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Arrested coalescence occurs in Pickering emulsions where colloidal particles adsorbed on the surface of the droplets become crowded and inhibit both relaxation of the droplet shape and further coalescence. The resulting droplets have a nonuniform distribution of curvature and, depending on the initial coverage, may incorporate a region with negative Gaussian curvature around the neck that bridges the two droplets. Here, we resolve the relative influence of the curvature and the kinetic process of arrest on the microstructure of the final state. In the quasistatic case, defects are induced and distributed to screen the Gaussian curvature. Conversely, if the rate of area change per particle exceeds the diffusion constant of the particles, the evolving surface induces local solidification reminiscent of jamming fronts observed in other colloidal systems. In this regime, the final structure is shown to be strongly affected by the compressive history just prior to arrest, which can be predicted from the extrinsic geometry of the sequence of surfaces in contrast to the intrinsic geometry that governs the static regime.