Recently I attended an introductory electromagnetism course where it was stated that a curved conductor surface can sustain a larger charge density than a flat conductor surface. Conventionally this phenomenon is explained by asserting that the parallel repulsive electric force between the electrons is smaller than at a level surface. However this parallel repulsive force is seemingly always caused by two oppositely located electrons (see the image below); but what about the repulsive force between neighboring electrons? To me it seems logical that the repulsive force between neighboring electrons, on a curved surface, must be far greater than that of neighboring electrons on a flat surface. Simply because those electrons are closer and therefore the Coulomb force must be greater.
All in all I would believe that the electrons on the flat surface should actually be closer to one another, however this is not the case. The conventional explanation seems incomplete/missing a few details, or perhaps I'm missing some key points.

[![/](https://i.stack.imgur.com/MB87E.png)](https://i.stack.imgur.com/MB87E.png)

Image source <https://courses.lumenlearning.com/physics/chapter/18-7-conductors-and-electric-fields-in-static-equilibrium>