charge density

This is because the potential on the surface of a conductor is constant. Charge density needs to be higher at sharp points, where the radius of surface curvature is small.

By V = kQ/R
where V is the potential,
k is a constant = 9x10^9 N-m^2/C^2
Q is the charge
R is the radius of curvature of the surface
Thus, Q = VR/k

Charge density p = Q/(4.pi.R^2) [ pi = 3.14159...]
hence p = (VR/k)/(4.pi.R^2) = V/(4.pi.k.R)
or V = 4.pi.k.R.p

To have the same potential throughout the conductor, it is claer that the smaller the radius of curvature of the surface(sharp points), the higher the charge density p, as (4.pi.k) is a constant.