In a negative pin-to-plate discharge in ambient air, three different modes can be observed: corona, glow and spark. The experimental results of this paper reveal the effect of the anode geometry on the extent of the glow regime. A quasi-two-dimensional model is applied to reconstruct the experimental current-voltage characteristics of negative corona discharges with curved anode surfaces. For a sufficiently large discharge current, the model yields a discharge structure that is similar to that of a low-pressure glow discharge.